GENERALIZED SOLUTIONS FOR FRACTIONAL SCHRÖDINGER EQUATION

GENERALIZED SOLUTIONS FOR FRACTIONAL SCHRÖDINGER EQUATION

A. Benmerrous, L. S. Chadli, A. Moujahid, M. Elomari, S. Melliani

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Abstract

This paper focuses on the fractional Schr¨odinger problem with the use of a new fractional derivative. Using Banach’s fixed point theorem and Laplace transforms, we give and prove the integral solution of the problem. In Colombeau’s algebra, The existence and uniqueness of the solution are demonstrated using the Gronwall lemma.

Keywords

Schr¨odinger problem, Distributions, Colombeau algebra, ψ−Caputo derivative, Laplace transforms.