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

Ibtehal Alazman; Mohamed Jleli; Bessem Samet; Ibtehal Alazman; Mohamed Jleli; Bessem Samet

doi:10.3934/math.2022323

AIMS Mathematics

2022, Volume 7, Issue 4: 5830-5843. doi: 10.3934/math.2022323

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

1.
Department of Mathematics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11566, Saudi Arabia
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

Received: 17 November 2021 Revised: 16 December 2021 Accepted: 20 December 2021 Published: 12 January 2022
MSC : 35B44, 34K37, 34A08

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.
- two-times fractional differential inequality,
- global solution,
- nonexistence,
- Hadamard-Caputo fractional derivative,
- Caputo fractional derivative
Citation: Ibtehal Alazman, Mohamed Jleli, Bessem Samet. On the absence of global solutions to two-times-fractional differential inequalities involving Hadamard-Caputo and Caputo fractional derivatives[J]. AIMS Mathematics, 2022, 7(4): 5830-5843. doi: 10.3934/math.2022323

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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.

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