Existence results for fractional neutral integro-differential systems with nonlocal condition through resolvent operators

Abstract

The manuscript is primarily concerned with the new existence results for fractional neutral integro-differential equation (FNIDE) with nonlocal conditions (NLCs) in Banach spaces. Based on the Banach contraction principle and Krasnoselskii fixed point theorem (FPT) joined with resolvent operators, we develop the main results. Ultimately, an representation is also offered to demonstrate the accomplished theorem.

Keywords

• fractional calculus
• integro-differential equations
• nonlocal condition
• resolvent operators
• banach and krasnoselskii fixed point theorem
• primary 34k30, 35r11, 26a33
• secondary 45k05, 47d06