A study of coupled systems of mixed order fractional differential equations and inclusions with coupled integral fractional boundary conditions

Abstract

Abstract In this work we investigate existence and uniqueness of solutions for new coupled systems of mixed order fractional differential equations and inclusions supplemented with coupled nonlocal fractional boundary conditions. We apply the Leray–Schauder alternative and the Banach contraction mapping principle to obtain the existence and uniqueness results, while in the multi-valued case we use the nonlinear alternative for Kakutani maps and Covitz and Nadler’s fixed point theorem.

Keywords

• Fractional differential equations
• Fractional differential inclusions
• System
• Mixed order
• Existence
• Fixed point