A Comprehensive Study of the Langevin Boundary Value Problems with Variable Order Fractional Derivatives-Reference-Cited by-同舟云学术

A Comprehensive Study of the Langevin Boundary Value Problems with Variable Order Fractional Derivatives

Published:2024-04-21 Issue:4 Volume:13 Page:277
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Graef John R.¹^ORCID,Maazouz Kadda²,Zaak Moussa Daif Allah²^ORCID

Affiliation:

1. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37401, USA

2. Department of Mathematics, University of Ibn Khaldoun, Tiaret 14000, Algeria

Abstract

The authors investigate Langevin boundary value problems containing a variable order Caputo fractional derivative. After presenting the background for the study, the authors provide the definitions, theorems, and lemmas that are required for comprehending the manuscript. The existence of solutions is proved using Schauder’s fixed point theorem; the uniqueness of solutions is obtained by adding an additional hypothesis and applying Banach’s contraction principle. An example is provided to demonstrate the results.

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/4/277/pdf

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