Nonexistence for fractional differential inequalities and systems in the sense of Erdélyi-Kober

Mohamed Jleli; Bessem Samet; Mohamed Jleli; Bessem Samet

doi:10.3934/math.20241055

AIMS Mathematics

2024, Volume 9, Issue 8: 21686-21702. doi: 10.3934/math.20241055

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Research article

Nonexistence for fractional differential inequalities and systems in the sense of Erdélyi-Kober

Mohamed Jleli ,
Bessem Samet ^,

Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Received: 27 April 2024 Revised: 14 June 2024 Accepted: 24 June 2024 Published: 08 July 2024
MSC : 26A33, 34A08, 34A12

Nonexistence theorems constitute an important part of the theory of differential and partial differential equations. Motivated by the numerous applications of fractional differential equations in diverse fields, in this paper, we studied sufficient conditions for the nonexistence of solutions (or, equivalently, necessary conditions for the existence of solutions) for nonlinear fractional differential inequalities and systems in the sense of Erdélyi-Kober. Our approach is based on nonlinear capacity estimates specifically adapted to the Erdélyi-Kober fractional operators and some integral inequalities.
- fractional differential inequalities,
- systems,
- Erdélyi-Kober fractional operators,
- nonexistence
Citation: Mohamed Jleli, Bessem Samet. Nonexistence for fractional differential inequalities and systems in the sense of Erdélyi-Kober[J]. AIMS Mathematics, 2024, 9(8): 21686-21702. doi: 10.3934/math.20241055

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Abstract

Nonexistence theorems constitute an important part of the theory of differential and partial differential equations. Motivated by the numerous applications of fractional differential equations in diverse fields, in this paper, we studied sufficient conditions for the nonexistence of solutions (or, equivalently, necessary conditions for the existence of solutions) for nonlinear fractional differential inequalities and systems in the sense of Erdélyi-Kober. Our approach is based on nonlinear capacity estimates specifically adapted to the Erdélyi-Kober fractional operators and some integral inequalities.

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