Best proximity point results and application to a system of integro-differential equations

Abstract

Abstract In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness. We first introduce the concept of cyclic (noncyclic) Θ-condensing operator for a pair of sets using the measure of noncompactness and then establish results on the best proximity pair (point) on Banach spaces and strictly Banach spaces. In addition, we have illustrated the considered system of integro-differential equations by three examples and discussed the stability, efficiency, and accuracy of solutions.

Keywords

• Best proximity point, measure of noncompactness (MNC)
• Darbo fixed point theorem (DFPT)
• Fractional calculus
• Fractional differential operator
• Fractional integral equation