GENERALIZED SOLUTIONS FOR TIME ψ-FRACTIONAL WAVE EQUATION

GENERALIZED SOLUTIONS FOR TIME ψ-FRACTIONAL WAVE EQUATION

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

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Abstract

This paper focuses on the fractional wave problem with the use of a new fractional derivative in Colombeau algebra. Using Banach's  xed 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

Fractional wave equation, ????Caputo derivative, Generalized solution, Laplace transforms, Singular data, Colombeau algebra.