Best proximity point theorems via measure of noncompactness and application to a system of Caputo fractional differential equations

Abstract

In this article, we establish a new best proximity point (pair) theorem for condensing operators defined on some new class of functions using the measure of noncompactness (MNC). Our theorem extends the  Darbo type fixed point theorem and some recent investigations in this direction. We apply our results to the study of optimum solutions for a system of Caputo fractional differential equations(FDEs).