Fractional nonlocal integro-differential equations with time-varying generating operators and optimal control

Abstract

A class of fractional integrodifferential equations of mixed type with time-varying generating operators and non-local conditions is considered. Using a contraction mapping principle and Krasnoselskiis fixed point theorem via Gronwall's inequality, the existence and uniqueness of the mild solution are given. The existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with time-varying generating operators and non-local conditions is also presented. That is, the chapter is to consider the following more general fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal initial conditions.