Affiliation:
1. Department of Mathematics, Faculty of Science Kuwait University P.O. Box 5969, Safat 13060, Kuwait
Abstract
Abstract
This paper is about the fractional Schrödinger equation expressed in terms of the Caputo time-fractional and quantum Riesz-Feller space fractional derivatives for particle moving in a potential field. The cases of free particle (zero potential) and a linear potential are considered. For free particle, the solution is obtained in terms of the Fox H-function. For the case of a linear potential, the separation of variables method allows the fractional Schrödinger equation to be split into space fractional and time fractional ones. By using the Fourier and Mellin transforms for the space equation and the contour integrals technique for the time equation, the solutions are obtained also in terms of the Fox H-function. Moreover, some recent results related to the time fractional equation have been revised and reconsidered. The results obtained in this paper contain as particular cases already known results for the fractional Schrödinger equation in terms of the quantum Riesz space-fractional derivative and standard Laplace operator.
Subject
Applied Mathematics,Analysis
Reference20 articles.
1. Andrews L.C., Special Functions of Mathematics for Engineers. 2nd Ed., Spie Press, Washington (1998).
2. Bayin S.S., Mathematical Methods in Science and Engineering. Wiley (2006).
3. Bayin S.S., Time fractional Schrödinger equation: Fox’s H-functions and the effective potential. J. Math. Phys. 54, No 1 (2013), Article # 012103; 10.1063/1.4773100.
4. Baqer S., Boyadjiev L., On the space-time fractional Schrödinger equation with time independent potentials. In: Contemporary Mathematics, 658, Amer. Math. Soc., Providence, RI (2016), 81–90.
5. Caputo M., Linear models of dissipation whose Q is almost frequency independent, II. Fract. Calc. Appl. Anal. 11, No 1 (2008), 4-14
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献