Blow-up of solutions to fractional differential inequalities involving $ \psi $-Caputo fractional derivatives of different orders

Ibtisam Aldawish; Mohamed Jleli; Bessem Samet; Ibtisam Aldawish; Mohamed Jleli; Bessem Samet

doi:10.3934/math.2022509

AIMS Mathematics

2022, Volume 7, Issue 5: 9189-9205. doi: 10.3934/math.2022509

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Research article

Blow-up of solutions to fractional differential inequalities involving $ \psi $-Caputo fractional derivatives of different orders

1.
Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammad Ibn Saud Islamic University), Riyadh, Saudi Arabia
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

Received: 16 November 2021 Revised: 29 January 2022 Accepted: 17 February 2022 Published: 09 March 2022
MSC : 34A08, 34K37, 35B44

We consider a fractional differential inequality involving $ \psi $-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\limits_{t\to \infty}\psi(t)=\infty $ and $ \lim\limits_{t\to \infty}\psi(t)<\infty $.
- fractional differential inequality,
- global solution,
- nonexistence,
- $ \psi $-Caputo fractional derivative,
- singular potential term
Citation: Ibtisam Aldawish, Mohamed Jleli, Bessem Samet. Blow-up of solutions to fractional differential inequalities involving $ \psi $-Caputo fractional derivatives of different orders[J]. AIMS Mathematics, 2022, 7(5): 9189-9205. doi: 10.3934/math.2022509

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Abstract

We consider a fractional differential inequality involving $ \psi $-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\limits_{t\to \infty}\psi(t)=\infty $ and $ \lim\limits_{t\to \infty}\psi(t)<\infty $.

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