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.
