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 - <p style="text-align: justify;">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&#39;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.</p>