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Research Article | Open Access

A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity

Mufit San( ), Seyma Ramazan
Department of Mathematics, Cankiri Karatekin University, Cankiri, Turkey
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Abstract

In this paper, we study an initial value problem with a weakly singular nonlinear fractional differential equation of higher order. First, we establish the existence of global solutions to the problem within the appropriate function space. We then introduce a generalized Riemann-Liouville mean value theorem. Using this theorem, we prove the Nagumo-type uniqueness theorem for the stated problem. Moreover, we give two examples to illustrate the applicability of the existence and uniqueness theorems.

Keywords

weakly singular integral equationfractional differential equationinitial value problemglobal existence

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Electronic Research Archive
Volume 32 Issue 5,
May 2024
Pages 3092-3112
DOI: 10.3934/era.2024141

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Cite this article:
San M, Ramazan S. A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity. Electronic Research Archive, 2024, 32(5): 3092-3112. https://doi.org/10.3934/era.2024141

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Received: 26 February 2024
Revised: 14 April 2024
Accepted: 17 April 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)