Existence results for a coupled system of (k,φ)-Hilfer fractional differential equations with nonlocal integro-multi-point boundary conditions

Abstract

In this paper, we investigate the existence and uniqueness of solutions to a nonlinear coupled systems of $ (k, \varphi) $-Hilfer fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions. We make use of the Banach contraction mapping principle to obtain the uniqueness result, while the existence results are proved with the aid of Krasnosel'ski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }} $'s fixed point theorem and Leray-Schauder alternative for the given problem. Examples demonstrating the application of the abstract results are also presented. Our results are of quite general nature and specialize in several new results for appropriate values of the parameters $ \beta_1, $ $ \beta_2, $ and the function $ \varphi $ involved in the problem at hand.

Keywords

• (k，φ)-hilfer fractional derivative
• riemann-liouville fractional derivative
• caputo fractional derivative
• existence
• uniqueness
• fixed point theorems