Existence and Stability of a Caputo Variable-Order Boundary Value Problem-Reference-Cited by-同舟云学术

Existence and Stability of a Caputo Variable-Order Boundary Value Problem

Published:2021-10-11 Issue: Volume:2021 Page:1-16
ISSN:2314-4785
Container-title:Journal of Mathematics
language:en
Short-container-title:Journal of Mathematics

Author:

Benkerrouche Amar¹,Souid Mohammed Said²,Chandok Sumit³^ORCID,Hakem Ali¹

Affiliation:

1. Laboratory ACEDP, Djillali Liabes University, Sidi Bel Abbès, Algeria

2. Department of Economic Sciences, University of Tiaret, Tiaret, Algeria

3. School of Mathematics, Thapar Institute of Engineering & Technology, Patiala 147004, India

Abstract

In this study, we investigate the existence of a solution to the boundary value problem (BVP) of variable-order Caputo-type fractional differential equation by converting it into an equivalent standard Caputo (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All our results in this study are proved by using Darbo’s fixed-point theorem and the Ulam–Hyers (UH) stability definition. A numerical example is given at the end to support and validate the potentiality of our obtained results.

Funder

NBHM-DAE

Publisher

Hindawi Limited

Subject

General Mathematics

Link

http://downloads.hindawi.com/journals/jmath/2021/7967880.pdf

Reference26 articles.

1. Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

2. Multivalued problems via orthogonal contraction mappings with application to fractional differential equation

3. A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems