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Solutions of Fractional Partial Differential Equations of Quantum Mechanics

Published online by Cambridge University Press:  03 June 2015

S. D. Purohit
S. D. Purohit*
Affiliation:
Department of Basic Sciences (Mathematics), College of Technology and Engineering, M.P. University of Agriculture and Technology, Udaipur-313001, India
*
*Corresponding author. Email: sunil_a_purohit@yahoo.com
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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.

Keywords

26A3344A1033C6035J10Fractional Schrödinger equationLaplace transformFourier transformHilfer fractional derivativeFox’s H-function and Quantum mechanics
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 5 , October 2013 , pp. 639 - 651
Copyright
Copyright © Global-Science Press 2013

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