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Existence of traveling profiles solutions to porous medium equation

Arioua Yacine, Benhamidouche Nouredine

Journal of Mathematics and Applications

2023

Vol. 46

149--162

In this paper, we shall study the existence and uniqueness of solutions called "traveling profiles solutions" to the porous medium equation in one dimension. By these solutions, we generalize the results obtained by Gilding and Peletier who proved the existence of self similar solutions of type I, II and III to the same equation. The principal idea of our work is to convert the porous media equation in to an equivalent nonlinear differential equation, and to prove the existence and uniqueness of these new solutions under certain conditions.

Existence and uniqueness of solutions for nonlinear Katugampola fractional differential equations

Basti Bilal, Arioua Yacine, Benhamidouche Nouredine

Journal of Mathematics and Applications

2019

Vol. 42

35--61

The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach fixed point theorems. For applications purposes, some examples are provided to demonstrate the usefulness of our main results.