Existence and uniqueness of solutions of fractional quasilinear mixed integrodifferential equations with nonlocal condition in Banach spaces

Abstract

In this paper, we discuss the existence and uniqueness of mild and classical solutions of quasilinear mixed integrodifferential equations of fractional orders with nonlocal condition in Banach spaces. Furthermore, we study continuous dependence of mild solutions. Our analysis is based on fractional calculus, resolvent operators and Banach's fixed point theorem.

Keywords

• existence and uniqueness
• mild and classical solutions
• fractional integrodifferential equation
• resolvent operators
• banach's fixed point theorem
• nonlocal condition