A novel implementation of fixed-point theorems for high-order Hadamard fractional differential equations with multi-point integral boundary conditions

Document Type : Research Article


Laboratory of Mathematics and Applied Sciences, University of Ghardaia, BP 455 Ghardaia 47000, Algeria


This research inscription gets to grips with a novel type of boundary value problem of nonlinear differential equations encapsuling a fractional derivative known as the Hadamard fractional operator. Our results rely on the standard tools of functional analysis. The existence of the solutions of the aforehand equations is tackled by using Schaefer and Krasnoselskii's fixed point theorems, whereas their uniqueness is handled using the Banach fixed point theorem. Two pertinent examples are presented to point out the applicability of our main results.


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