In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed po...In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed point theorem, Banach contraction principle and Ulam type stability.展开更多
In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hi...In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.展开更多
The aimof this article is to investigate the solutions of generalized fractional partial differential equations involving Hilfer time fractional derivative and the space fractional generalized Laplace operators,occurr...The aimof this article is to investigate the solutions of generalized fractional partial differential equations involving Hilfer time fractional derivative and the space fractional generalized Laplace operators,occurring in quantum mechanics.The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms,in terms of the Fox’s H-function.Several special cases as solutions of one dimensional non-homogeneous fractional equations occurring in the quantum mechanics are presented.The results given earlier by Saxena et al.[Fract.Calc.Appl.Anal.,13(2)(2010),pp.177-190]and Purohit and Kalla[J.Phys.AMath.Theor.,44(4)(2011),045202]follow as special cases of our findings.展开更多
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,Saudi Arabia under grant no.KEP-Msc-9-130-39
文摘In this paper, we discuss the existence, uniqueness and stability of boundary value problem for differential equation with Hilfer-Katugampola fractional derivative. The arguments are based upon Schaefer's fixed point theorem, Banach contraction principle and Ulam type stability.
文摘In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.
基金The author thanks the referees for his/her suggestions,which improved the presentation of this paper.Also,the author thanks Professor S.L.Kalla for his valuable suggestions and criticisms.
文摘The aimof this article is to investigate the solutions of generalized fractional partial differential equations involving Hilfer time fractional derivative and the space fractional generalized Laplace operators,occurring in quantum mechanics.The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms,in terms of the Fox’s H-function.Several special cases as solutions of one dimensional non-homogeneous fractional equations occurring in the quantum mechanics are presented.The results given earlier by Saxena et al.[Fract.Calc.Appl.Anal.,13(2)(2010),pp.177-190]and Purohit and Kalla[J.Phys.AMath.Theor.,44(4)(2011),045202]follow as special cases of our findings.
