ON A FRACTIONAL WAVE EQUATION WITH SINGULAR INITIAL DATA

ON A FRACTIONAL WAVE EQUATION WITH SINGULAR INITIAL DATA

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

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Abstract

This paper focuses on the time fractional wave equation with the use of conformable derivative D(α) for 1 < α < 2 which we will prove to be inside Colombeau algebra, the initial data are singular distibution. Nets of conformable cosine family (Cα ϵ )ϵ with polynomial development in ϵ as ϵ → 0 are defined for the first time and used for solving this irregular fractional problems.

Keywords

Fractional wave equation, Colombeau algebra, Conformable cosine family, Generalized function.