On a fractional wave equation with singular initial data

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 (Cαϵ )ϵ with polynomial development in ϵ as ϵ → 0 are defined for the first time and used for solving this irregular fractional problems.