Coupled Fractional-Order Systems with Nonlocal Coupled Integral and Discrete Boundary Conditions

Abstract

In this paper, we study a coupled system of Caputo fractional differential equations with nonlinearities depending on the unknown functions as well as their derivatives, equipped with new kinds of integral and multi-point (discrete) boundary conditions. In fact, we have introduced the idea of unification of coupled strip and multi-point boundary conditions with their different variants in the present work. Though we apply the standard tools of the fixed point theory to develop the existence criteria for the solutions of given problems, the obtained results are new in the given scenario. Some examples illustrating the main results are also presented.