A novel extension of Darbo's fixed point theorem and its application to a class of differential equations involving (k,ψ)-Hilfer fractional derivative

Abstract

In this article, a new generalised class of operators called as A-condensing operators is introduced. The fixed point as well as coupled fixed point results are established for the newly defined class of mappings. The rich theory of measure of noncompactness is utilized in this purpose. The new results extend some of the famous works in the literature. Finally, an application to (k,ψ)-Hilfer fractional differential equation of order 2<p<3 and type 0 ≤ q ≤ 1 is presented.