A formalized calculus system called F_fuzzy calculus system, which is a symbol deduction system to formalize fuzzy inference, is constructed in this paper. The fuzzy modus ponens was completely formalized in this calc...A formalized calculus system called F_fuzzy calculus system, which is a symbol deduction system to formalize fuzzy inference, is constructed in this paper. The fuzzy modus ponens was completely formalized in this calculus system.展开更多
Based on the fact that the real inductor and the real capacitor are fractional order in nature and the fractional calculus,the transfer function modeling and analysis of the open-loop Buck converter in a continuous co...Based on the fact that the real inductor and the real capacitor are fractional order in nature and the fractional calculus,the transfer function modeling and analysis of the open-loop Buck converter in a continuous conduction mode（CCM） operation are carried out in this paper.The fractional order small signal model and the corresponding equivalent circuit of the open-loop Buck converter in a CCM operation are presented.The transfer functions from the input voltage to the output voltage,from the input voltage to the inductor current,from the duty cycle to the output voltage,from the duty cycle to the inductor current,and the output impedance of the open-loop Buck converter in CCM operation are derived,and their bode diagrams and step responses are calculated,respectively.It is found that all the derived fractional order transfer functions of the system are influenced by the fractional orders of the inductor and the capacitor.Finally,the realization of the fractional order inductor and the fractional order capacitor is designed,and the corresponding PSIM circuit simulation results of the open-loop Buck converter in CCM operation are given to confirm the correctness of the derivations and the theoretical analysis.展开更多
The Open Flow implementations(SDNs) have been deployed increasingly on varieties of networks in research institutions as well as commercial institutions. To develop an Open Flow implementation, it is required to under...The Open Flow implementations(SDNs) have been deployed increasingly on varieties of networks in research institutions as well as commercial institutions. To develop an Open Flow implementation, it is required to understand the performance of the network. A few benchmark tools(e.g., Cbench and OFlops) can be used to measure the network performance, while these tools take considerable time to simulate traffic behaviors and generate the required results,therefore extending the development time. In this paper, we present an analytical model, which is based on stochastic network calculus theory, for evaluating the performance of switch to controller.The previous studies show that stochastic network calculus can provide realistic emulation of real network traffic behaviors. Our model is evaluated by using both simulation tool and realistic testbed.The results show the stochastic network calculus based analysis model can realistically measure the network performance of the end-to-end properties between controller and switch.展开更多
By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As a...By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.展开更多
In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find seve...In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.展开更多
Trajectory provides the most robust feature for activity recognition in far-field surveillance videos,in which increasing attentions have been given to the use of qualitative methods with symbolic rather than real-val...Trajectory provides the most robust feature for activity recognition in far-field surveillance videos,in which increasing attentions have been given to the use of qualitative methods with symbolic rather than real-value features.Qualitative trajectory calculus(QTC)showed a good performance in pair-activity from video.However,QTC and similar works are not good at dealing with noise,since they are all considering short-term features.To deal with the problems mentioned above,two types of long-term features,including sub-trajectory feature and point-trajectory feature,are designed.The sub-trajectory feature is a long-term feature in a coarse granularity,while the point-trajectory feature is a long-term feature in a relatively fine granularity.Using the sub-trajectory feature,a couple of trajectories are segmented into sub-trajectories and enveloping boxes are used to substitute the original sub-trajectory for capturing the major attributes.The point-trajectory feature describes the relationship between a single point in one trajectory and all parts of the other trajectory.The experiments on the human activity classification data demonstrated that our proposed methods are better than the original QTC and previous short-term features.展开更多
Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s res...Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.展开更多
Network calculus is an evolving new methodology for backlog and delay analysis of packet-switching networks. With network calculus we are able to compute tight bounds on delays,backlogs,and effective bandwidths in a l...Network calculus is an evolving new methodology for backlog and delay analysis of packet-switching networks. With network calculus we are able to compute tight bounds on delays,backlogs,and effective bandwidths in a lossless setting applicable to packet-switching networks and better understand some physical properties of networks. In this paper,the basic network calculus concepts of arrival curves and service curves are introduced.Then we provide the approach for modeling leaky-bucket,generic cell rate algorithm(GCRA),constant bit rate(CBR)flow, variable bit rate(VBR) flow with arrival curve.It is shown that all rate-based packet schedulers can be by a simple rate latency service curve.And by applying these fundamental rules of network calculus,bounds on delay, buffer,effective bandwidth for leaky bucket,GCRA,CBR and VBR can be derived and some practical examples are given.Finally,we compare all the results obtained and conclude this paper.展开更多
In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide a...In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.展开更多
The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-fun...The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.展开更多
The Landau equation is studied for hard potential with-2≤γ≤1.Under a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_...The Landau equation is studied for hard potential with-2≤γ≤1.Under a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_(v)^(2)(d>3/2),which extends the results of[11]in the torus domain to the whole space R_(x)^(3).Here we utilize the pseudo-differential calculus to derive our desired result.展开更多
We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach.We first show the global wellposedness in the Sobolev space H^(2)(R^(3)) for solu...We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach.We first show the global wellposedness in the Sobolev space H^(2)(R^(3)) for solutions near equilibrium through iterated energy-type bounds and a continuity argument.We then prove the global well-posedness in the critical Besov space B^(3/2)_(2,1) by showing that the linearized operator is a contraction mapping under the right circumstances.展开更多
In recent years,various internet architectures,such as Integrated Services(IntServ),Differentiated Services(DiffServ),Time Sensitive Networking(TSN)and Deterministic Networking(DetNet),have been proposed to meet the q...In recent years,various internet architectures,such as Integrated Services(IntServ),Differentiated Services(DiffServ),Time Sensitive Networking(TSN)and Deterministic Networking(DetNet),have been proposed to meet the quality-of-service(QoS)requirements of different network services.Concurrently,network calculus has found widespread application in network modeling and QoS analysis.Network calculus abstracts the details of how nodes or networks process data packets using the concept of service curves.This paper summarizes the service curves for typical scheduling algorithms,including Strict Priority(SP),Round Robin(RR),Cycling Queuing and Forwarding(CQF),Time Aware Shaper(TAS),Credit Based Shaper(CBS),and Asynchronous Traffic Shaper(ATS).It introduces the theory of network calculus and then provides an overview of various scheduling algorithms and their associated service curves.The delay bound analysis for different scheduling algorithms in specific scenarios is also conducted for more insights.展开更多
Autonomy, a key property associated with the agent, is an important topic in the current research of the agent theory. Although no definition of the agent autonomy is universally accepted, an important aspect of the a...Autonomy, a key property associated with the agent, is an important topic in the current research of the agent theory. Although no definition of the agent autonomy is universally accepted, an important aspect of the agent autonomy is the decision-making capability of the agents. This paper investigates the autonomy of the agent, presents a framework for autonomous agent and discusses its decision-making process. Started with introducing a language for representing autonomous agent, a framework is proposed for modeling autonomous agent based on a BDI model and the situation calculus. Finally, a kind of decision-making process of the autonomous agent is presented.展开更多
In this paper we numerically investigate the chaotic behaviours of the fractional-order Ikeda delay system. The results show that chaos exists in the fractional-order Ikeda delay system with order less than 1. The low...In this paper we numerically investigate the chaotic behaviours of the fractional-order Ikeda delay system. The results show that chaos exists in the fractional-order Ikeda delay system with order less than 1. The lowest order for chaos to be a, ble to appear in this system is found to be 0.1. Master-slave synchronization of chaotic fractional-order Ikeda delay systems with linear coupling is also studied.展开更多
AOPLID is a novel agent oriented programming language whose theoretical framework is the existed situation calculus theory and agent model based on intention driven manner. An AOPLID program is represented in set ma...AOPLID is a novel agent oriented programming language whose theoretical framework is the existed situation calculus theory and agent model based on intention driven manner. An AOPLID program is represented in set manner. In this paper, an off line AOPLID interpreter in Prolog is implemented, based on the off line AOPLID program semantics. At the same time, the set of rules is given which transforms an AOPLID program represented by sets into Prolog clauses so that it can be interpreted by the off line interpreter. Finally, the sound codes of the off line interpreter are listed.展开更多
′In this article, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved （G′/G）-expansion func...′In this article, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved （G′/G）-expansion function method to calculate the exact solutions to the time- and space-fractional derivative foam drainage equation and the time- and space-fractional derivative nonlinear KdV equation. This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.展开更多
The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary order,is presented in this paper.The reasons why the generalized...The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary order,is presented in this paper.The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained.K-index,P-index,O-index,and complexity index are introduced to contribute to performance analysis.Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order,these rational approximation impedance functions calculated by the iterating function meet computational rationality,positive reality,and operational validity.Then they are capable of having the operational performance of fractional operators and being physical realization.The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited.展开更多
In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak to...In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.展开更多
In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractiona...In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.展开更多
文摘A formalized calculus system called F_fuzzy calculus system, which is a symbol deduction system to formalize fuzzy inference, is constructed in this paper. The fuzzy modus ponens was completely formalized in this calculus system.
基金Project supported by the National Natural Science Foundation of China (Grant No. 51007068)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100201120028)+2 种基金the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2012JQ7026)the Fundamental Research Funds for the Central Universities of China (Grant No. 2012jdgz09)the State Key Laboratory of Electrical Insulation and Power Equipment of China (Grant No. EIPE12303)
文摘Based on the fact that the real inductor and the real capacitor are fractional order in nature and the fractional calculus,the transfer function modeling and analysis of the open-loop Buck converter in a continuous conduction mode（CCM） operation are carried out in this paper.The fractional order small signal model and the corresponding equivalent circuit of the open-loop Buck converter in a CCM operation are presented.The transfer functions from the input voltage to the output voltage,from the input voltage to the inductor current,from the duty cycle to the output voltage,from the duty cycle to the inductor current,and the output impedance of the open-loop Buck converter in CCM operation are derived,and their bode diagrams and step responses are calculated,respectively.It is found that all the derived fractional order transfer functions of the system are influenced by the fractional orders of the inductor and the capacitor.Finally,the realization of the fractional order inductor and the fractional order capacitor is designed,and the corresponding PSIM circuit simulation results of the open-loop Buck converter in CCM operation are given to confirm the correctness of the derivations and the theoretical analysis.
基金supported by the National Science and Technology Support Program (2014BAH24F01)the National Basic Research Program of China(2012CB3 15903)+3 种基金the Program for Key Science and Technology Innovation Team of Zhejiang Province (2011R50010-21,2013TD20)863 Program of China(2015AA015602,2015AA016103)the National Natural Science Foundation of China (61379118)the Fundamental Research Funds for the Central Universities
文摘The Open Flow implementations(SDNs) have been deployed increasingly on varieties of networks in research institutions as well as commercial institutions. To develop an Open Flow implementation, it is required to understand the performance of the network. A few benchmark tools(e.g., Cbench and OFlops) can be used to measure the network performance, while these tools take considerable time to simulate traffic behaviors and generate the required results,therefore extending the development time. In this paper, we present an analytical model, which is based on stochastic network calculus theory, for evaluating the performance of switch to controller.The previous studies show that stochastic network calculus can provide realistic emulation of real network traffic behaviors. Our model is evaluated by using both simulation tool and realistic testbed.The results show the stochastic network calculus based analysis model can realistically measure the network performance of the end-to-end properties between controller and switch.
基金Supported by the China Pcetdoctoral Science Foundation by a grant from Henan University(05YBZR014)Supported by the Tianyuan Foundation for Mathematics of National Natural Science Foundation of China(10626016)
文摘By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.
文摘In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.
基金Supported by the National Natural Science Foundation of China(61502198)
文摘Trajectory provides the most robust feature for activity recognition in far-field surveillance videos,in which increasing attentions have been given to the use of qualitative methods with symbolic rather than real-value features.Qualitative trajectory calculus(QTC)showed a good performance in pair-activity from video.However,QTC and similar works are not good at dealing with noise,since they are all considering short-term features.To deal with the problems mentioned above,two types of long-term features,including sub-trajectory feature and point-trajectory feature,are designed.The sub-trajectory feature is a long-term feature in a coarse granularity,while the point-trajectory feature is a long-term feature in a relatively fine granularity.Using the sub-trajectory feature,a couple of trajectories are segmented into sub-trajectories and enveloping boxes are used to substitute the original sub-trajectory for capturing the major attributes.The point-trajectory feature describes the relationship between a single point in one trajectory and all parts of the other trajectory.The experiments on the human activity classification data demonstrated that our proposed methods are better than the original QTC and previous short-term features.
文摘Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.
基金supported in part by the development Foundation of Southwest Jiaotong Universitythe National Natural Science Foundation of China under Grant No.60572143
文摘Network calculus is an evolving new methodology for backlog and delay analysis of packet-switching networks. With network calculus we are able to compute tight bounds on delays,backlogs,and effective bandwidths in a lossless setting applicable to packet-switching networks and better understand some physical properties of networks. In this paper,the basic network calculus concepts of arrival curves and service curves are introduced.Then we provide the approach for modeling leaky-bucket,generic cell rate algorithm(GCRA),constant bit rate(CBR)flow, variable bit rate(VBR) flow with arrival curve.It is shown that all rate-based packet schedulers can be by a simple rate latency service curve.And by applying these fundamental rules of network calculus,bounds on delay, buffer,effective bandwidth for leaky bucket,GCRA,CBR and VBR can be derived and some practical examples are given.Finally,we compare all the results obtained and conclude this paper.
基金supported by FEDER funds through COMPETE - Operational Programme Factors of Competitiveness("Programa Operacional Factores de Competitividade")Portuguese funds through the Center for Research and Development in Mathematics and Applications(University of Aveiro) and the Portuguese Foundation for Science and Technology("FCT - Fundao para a Ciencia e a Tecnologia"),within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690
文摘In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.
基金NBHM Department of Atomic Energy,Government of India,Mumbai for the finanicai assistance under PDF sanction no.2/40(37)/2014/R&D-II/14131
文摘The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.
文摘The Landau equation is studied for hard potential with-2≤γ≤1.Under a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_(v)^(2)(d>3/2),which extends the results of[11]in the torus domain to the whole space R_(x)^(3).Here we utilize the pseudo-differential calculus to derive our desired result.
基金partially supported by the Zhejiang Province Science Fund(LY21A010009)partially supported by the National Science Foundation of China(12271487,12171097)partially supported by the National Science Foundation(DMS-2012333,DMS-2108209)。
文摘We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach.We first show the global wellposedness in the Sobolev space H^(2)(R^(3)) for solutions near equilibrium through iterated energy-type bounds and a continuity argument.We then prove the global well-posedness in the critical Besov space B^(3/2)_(2,1) by showing that the linearized operator is a contraction mapping under the right circumstances.
基金supported by ZTE Industry-University-Institute Cooperation Funds。
文摘In recent years,various internet architectures,such as Integrated Services(IntServ),Differentiated Services(DiffServ),Time Sensitive Networking(TSN)and Deterministic Networking(DetNet),have been proposed to meet the quality-of-service(QoS)requirements of different network services.Concurrently,network calculus has found widespread application in network modeling and QoS analysis.Network calculus abstracts the details of how nodes or networks process data packets using the concept of service curves.This paper summarizes the service curves for typical scheduling algorithms,including Strict Priority(SP),Round Robin(RR),Cycling Queuing and Forwarding(CQF),Time Aware Shaper(TAS),Credit Based Shaper(CBS),and Asynchronous Traffic Shaper(ATS).It introduces the theory of network calculus and then provides an overview of various scheduling algorithms and their associated service curves.The delay bound analysis for different scheduling algorithms in specific scenarios is also conducted for more insights.
文摘Autonomy, a key property associated with the agent, is an important topic in the current research of the agent theory. Although no definition of the agent autonomy is universally accepted, an important aspect of the agent autonomy is the decision-making capability of the agents. This paper investigates the autonomy of the agent, presents a framework for autonomous agent and discusses its decision-making process. Started with introducing a language for representing autonomous agent, a framework is proposed for modeling autonomous agent based on a BDI model and the situation calculus. Finally, a kind of decision-making process of the autonomous agent is presented.
基金Project supported by the National Natural Science Foundation of China （Grant No 60404005）.
文摘In this paper we numerically investigate the chaotic behaviours of the fractional-order Ikeda delay system. The results show that chaos exists in the fractional-order Ikeda delay system with order less than 1. The lowest order for chaos to be a, ble to appear in this system is found to be 0.1. Master-slave synchronization of chaotic fractional-order Ikeda delay systems with linear coupling is also studied.
文摘AOPLID is a novel agent oriented programming language whose theoretical framework is the existed situation calculus theory and agent model based on intention driven manner. An AOPLID program is represented in set manner. In this paper, an off line AOPLID interpreter in Prolog is implemented, based on the off line AOPLID program semantics. At the same time, the set of rules is given which transforms an AOPLID program represented by sets into Prolog clauses so that it can be interpreted by the off line interpreter. Finally, the sound codes of the off line interpreter are listed.
文摘′In this article, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved （G′/G）-expansion function method to calculate the exact solutions to the time- and space-fractional derivative foam drainage equation and the time- and space-fractional derivative nonlinear KdV equation. This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.
文摘The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary order,is presented in this paper.The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained.K-index,P-index,O-index,and complexity index are introduced to contribute to performance analysis.Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order,these rational approximation impedance functions calculated by the iterating function meet computational rationality,positive reality,and operational validity.Then they are capable of having the operational performance of fractional operators and being physical realization.The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited.
文摘In this article, we investigate the existence of Pseudo solutions for some fractional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.
基金the Council of Scientific and Industrial Research(CSIR),India
文摘In this work, a theory of thermoelasticity with diffusion is taken into consideration by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order generalized thermoelastic diffusive medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in the homogeneous transversely isotropic thermoelastic diffusive medium with fractional order derivative is studied. For the two-dimensional problem, there exist a quasi-longitudinal wave, a quasi-transverse wave, a quasi-mass diffusion wave, and a quasi-thermal wave. From the obtained results, the different characteristics of waves, like phase velocity, attenuation coefficient, specific loss, and penetration depth, are computed numerically and presented graphically. Some special cases are also discussed.
