Solvability of a Nonlocal Integral Problem of a Mixed Type Derivatives Functional Integro-Differential Equation

In this work, we study a nonlocal integral problem of a mixed-type (integer and fractional-order derivatives) functional integro-differential equation. The existence of absolutely continuous nondecreasing solutions will be proved. The sufficient conditions for the uniqueness of the solution will be given. The continuous dependence of the unique solution, on the parameters of the problem will be proved. Finally, Hyers-Ulam stability of the problem itself will be studied.