Solution to Fractional Schrödinger and Airy Differential Equations via Integral Transforms
A. Aghili *
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan P. O. Box-1841, Rasht, Iran.
H. Zeinali
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan P. O. Box-1841, Rasht, Iran.
*Author to whom correspondence should be addressed.
Abstract
Due to the need and the necessity to express a physical phenomenon in terms of an effective and comprehensive analytical form, this paper is devoted to study of Airy functions, which arise from the Airy differential equations, by means of integral transforms. Illustrative examples are also provided. The result reveals that the integral transforms are very useful tools to solve differential equations.
Keywords: Laplace transform, Fourier transform, L2 – transform, airy functions, fractional airy differential equations, Schrödinger equation.