Solvability of a Nonlocal Integral Problem of Integro-Mixed-Differential Equation Constrained by a Nonlinear Caputo-Fractional Order Constraint

In this work, we study the constrained problem of a nonlocal integral problem of a functional integrodifferential (mixed integer and fractional) equation under a nonlinear Caputo fractional order constraint. The existence of solutions will be proved. The sufficient conditions for uniqueness will be given. Moreover, we analyze the continuous dependence of the unique solution on some parameters. Further, we investigate the Hyers-Ulam stability of the problem.