On a coupled system of fractional differential equations with a new class of nonlocal strip boundary conditions

On a coupled system of fractional differential equations

Résumé

In this paper, we introduce and study a novel class of boundary value problems for a coupled system of two nonlinear fractional differential equations supplemented with strip boundary conditions occupying the initial and final segments $[0, \xi]$ and $[\eta, T]$ of the domain $[0, T]$ such that the values of the unknown functions behave differently within and at the end points of the strips. We apply Leray-Schauder's alternative and Banach's fixed point theorem to derive the existence and uniqueness results for the given problem. Though we employ the standard fixed point theorems to study the given problem, yet the application of these tools of the fixed point theory provides a useful strategy to explore its solution characteristics. We also discuss the Ulam-Hyers stability of the problem at hand. Examples illustrating the obtained results are offered.