ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Existence and Uniqueness Solutions of a BVP for Nonlinear Caputo-Hadamard Fractional Differential Equation

Journal of Applied Nonlinear Dynamics 11(2) (2022) 359--374 | DOI:10.5890/JAND.2022.06.007

Abdelatif Boutiara$^1$, Maamar Benbachir$^2$, Kaddour Guerbati$^1$

$^1$ Laboratoire de Math\'{e}matiques et Sciences appliqu\'{e}es, University of Ghardaia, Algeria

$^2$ Faculty of Sciences, Saad Dahlab University, Blida 1, Algeria

Abstract

In this paper, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem with Caputo-Hadamard derivative. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer's and krasnoselskii's fixed point theorems. At the end, some illustrative examples are presented.

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