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Solutions of Fractional Partial Differential Equations of Quantum Mechanics

Solutions of Fractional Partial Differential Equations of Quantum Mechanics
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Year:    2013

Author:    S. D. Purohit

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 5 : pp. 639–651

Abstract

The aim of 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. A Math. Theor., 44 (4) (2011), 045202] follow as special cases of our findings.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.12-m1298

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 5 : pp. 639–651

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Fractional Schrödinger equation Laplace transform Fourier transform Hilfer fractional derivative Fox's $H$-function and Quantum mechanics.

Author Details

S. D. Purohit

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