Solutions of Fractional Partial Differential Equations of Quantum Mechanics (Advances in Applied Mathematics and Mechanics, 2013)
The aim of this article is to investigate the solutions of generalized fractionalpartial differential equations involving Hilfer time fractional derivative and thespace fractional generalized Laplace operators, occurring in quantum mechanics. Thesolutions of these equations are obtained by employing the joint Laplace and Fouriertransforms, in terms of the Fox's $H$-function. Several special cases as solutions ofone dimensional non-homogeneous fractional equations occurring in the quantum mechanicsare presented. The results given earlier by Saxenaet 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.