Holder's Inequality ρ-Mean Continuity for Existence and Uniqueness Solution of Fractional Multi-Integrodifferential Delay System

We herein present the detailed results for the existence and uniqueness of mild solution for multifractional order impulsive integrodifferential control equations with a nonlocal condition involving several types of semigroups of bounded linear operators, which were established on probability density functions related with the fractional differential equation. Additionally, we present the necessary and sufficient conditions to investigate Schauder's fixed point theorem with Holder's inequality rho-mean continuity and infinite delay parameter to guarantee the uniqueness of a fixed point.