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Research Article | Open Access

Blow-up of solutions to fractional differential inequalities involving ψ-Caputo fractional derivatives of different orders

Ibtisam Aldawish1, Mohamed Jleli2, Bessem Samet2( )
Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammad Ibn Saud Islamic University), Riyadh, Saudi Arabia
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia
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Abstract

We consider a fractional differential inequality involving ψ-Caputo fractional derivatives of different orders, with a polynomial nonlinearity and a singular potential term. Using the test function method and some integral inequalities, we establish nonexistence criteria of global solutions in both cases: lim t → ∞ ψ ( t ) = ∞ and lim t → ∞ ψ ( t ) < ∞.

Keywords

fractional differential inequalityglobal solutionnonexistenceψ-Caputo fractional derivativesingular potential term
CLC number: 34A08, 34K37, 35B44

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 9189-9205
DOI: 10.3934/math.2022509

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Cite this article:
Aldawish I, Jleli M, Samet B. Blow-up of solutions to fractional differential inequalities involving ψ-Caputo fractional derivatives of different orders. AIMS Mathematics, 2022, 7(5): 9189-9205. https://doi.org/10.3934/math.2022509

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Received: 16 November 2021
Revised: 29 January 2022
Accepted: 17 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

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