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Existence of solutions for a three-point Hadamard fractional resonant boundary value problem

Gholami Yousef

Journal of Applied Analysis

2023

Vol. 29, nr 1

31--47

This article focuses on the creation of an existence theorem for a fully nonlinear Hadamard fractional boundary value problem subject to special three-point boundary conditions. By making use of the coincidence degree theory, it is proved that our governing problem makes resonance, that is, the linear part of the differential operator is non-invertible (equally, the corresponding linear problem has at least one nontrivial solution). Constructing some hypotheses on the linear part of the differential operator, nonlinearities and boundary conditions, we give an existence criterion for at least one solution of the fractional-order resonant boundary value problem under study. At the end, a numerical example is presented to illustrate the obtained theoretical results.

L1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative

Telli Benoumran, Souid Mohammed Said

Journal of Applied Analysis

2022

Vol. 28, nr 1

1--9

In this paper, we study the existence of integrable solutions for initial value problems for fractional order implicit differential equations with Hadamard fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.