Existence analysis on a $(k , \varphi)$-Hilfer FBVPs with a linear combination of $(k , \varphi)$-Hilfer derivatives

Abstract

In this paper, we apply classical Banach and Krasnosel'ski\u{i}'s fixed point theorems along with Leray-Schauder alternative to study the existence and uniqueness of solutions for FDEs involving $(k, \varphi)$-Hilfer fractional derivative with a linear combination of two $(k , \varphi)$-Hilfer derivatives in boundary value conditions. Finally, we present some examples to validate our theoretical outcomes.