Systems of Sequential ψ1-Hilfer and ψ2-Caputo Fractional Differential Equations with Fractional Integro-Differential Nonlocal Boundary Conditions

In this paper, we introduce and study a new class of coupled and uncoupled systems, consisting of mixed-type ?(1)-Hilfer and ?(2)-Caputo fractional differential equations supplemented with asymmetric and symmetric integro-differential nonlocal boundary conditions (systems (2) and (13), respectively). As far as we know, this combination of ?(1)-Hilfer and ?(2)-Caputo fractional derivatives in coupled systems is new in the literature. The uniqueness result is achieved via the Banach contraction mapping principle, while the existence result is established by applying the Leray-Schauder alternative. Numerical examples illustrating the obtained results are also presented.