Authors: Yacine Arioua ; Maria Titraoui

In this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel’skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness of our main results.

• 34A08 - Fractional ordinary differential equations
• 34A37 - Ordinary differential equations with impulses
• 47H10 - Fixed-point theorems