This article is devoted to establishing the existence and uniqueness of solutions to the fractional problem of diffusion waves in the following Colombeau algebra: cases Dₜ^ u (x, t) + ₓ u (x, t) = f (t, u (t, x) ) ; (x, t) 0, T \\ u (0, x) = ₀ (x) = (x) ; \\ ₜ u (0, x) = ₁ (x). cases. Where Dₜ^ is the fractionnal derivative with 1 <? < 2,? is the Laplace operator, ₀, ₁ are generalized functions,? is distributions and Rⁿ. This study is based on the integral solution of this problem using the Gronwall? s lemma. Finally we study the association concept with the classical solution.
Sadek et al. (Wed,) studied this question.