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Volume 5, Issue 5
Solutions of Fractional Partial Differential Equations of Quantum Mechanics

S. D. Purohit

Adv. Appl. Math. Mech., 5 (2013), pp. 639-651.

Published online: 2013-05

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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.

  • AMS Subject Headings

26A33, 44A10, 33C60, 35J10

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COPYRIGHT: © Global Science Press

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@Article{AAMM-5-639, author = {Purohit , S. D.}, title = {Solutions of Fractional Partial Differential Equations of Quantum Mechanics}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m1298}, url = {http://global-sci.org/intro/article_detail/aamm/89.html} }
TY - JOUR T1 - Solutions of Fractional Partial Differential Equations of Quantum Mechanics AU - Purohit , S. D. JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 639 EP - 651 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.12-m1298 UR - https://global-sci.org/intro/article_detail/aamm/89.html KW - Fractional Schrödinger equation, Laplace transform, Fourier transform, Hilfer fractional derivative, Fox's $H$-function and Quantum mechanics. AB -

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.

S. D. Purohit. (1970). Solutions of Fractional Partial Differential Equations of Quantum Mechanics. Advances in Applied Mathematics and Mechanics. 5 (5). 639-651. doi:10.4208/aamm.12-m1298
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