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Research Article | Open Access

On the absence of global solutions to two-times-fractional differential inequalities involving Hadamard-Caputo and Caputo fractional derivatives

Ibtehal Alazman1, Mohamed Jleli2, Bessem Samet2( )
Department of Mathematics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11566, Saudi Arabia
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia
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Abstract

In this paper, we consider a two-times nonlinear fractional differential inequality involving both Hadamard-Caputo and Caputo fractional derivatives of different orders, with a singular potential term. We obtain sufficient criteria depending on the parameters of the problem, for which a global solution does not exist. Some examples are provided to support our main results.

Keywords

two-times fractional differential inequalityglobal solutionnonexistenceHadamard-Caputo fractional derivativeCaputo fractional derivative
CLC number: 35B44, 34K37, 34A08

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 5830-5843
DOI: 10.3934/math.2022323

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Cite this article:
Alazman I, Jleli M, Samet B. On the absence of global solutions to two-times-fractional differential inequalities involving Hadamard-Caputo and Caputo fractional derivatives. AIMS Mathematics, 2022, 7(4): 5830-5843. https://doi.org/10.3934/math.2022323

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Received: 17 November 2021
Revised: 16 December 2021
Accepted: 20 December 2021
Published: 15 April 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)