Studies on existence results for fractional order neutral integro differential systems in banach spaces

Abstract

The research reported in this thesis deals with the problem of existence results for various types of fractional neutral differential and integro differential systems with nonlocal conditions in Banach spaces We first study the existence of mild solutions for an impulsive fractional neutral integro differential equations with nonlocal conditions in Banach spaces Next existence of mild solutions for an impulsive fractional evolution integro differential inclusions with nonlocal conditions in Banach spaces are discussed Then we analyze the existence of mild solutions for an impulsive fractional evolution integro differential systems with nonlocal conditions through are solvent operator Further more we discuss the existence of mild solutions for an impulsive fractional neutral integro differential equations with nonlocal conditions via aresolvent operator Finally a new class of Caputo Hadamard sequential fractional neutral functional integro differential systems in Banach spaces are discussed Our approach here is based on the fixed point techniques Several examples are provided to illustrate the obtained results newline