Nonlinear fractional differential inclusions with non-singular Mittag-Leffler kernel

Mohamed I. Abbas; Maria Alessandra Ragusa; Mohamed I. Abbas; Maria Alessandra Ragusa

doi:10.3934/math.20221113

AIMS Mathematics

2022, Volume 7, Issue 11: 20328-20340. doi: 10.3934/math.20221113

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Research article

Nonlinear fractional differential inclusions with non-singular Mittag-Leffler kernel

Mohamed I. Abbas ¹,
Maria Alessandra Ragusa ^{2
,
,}

1.
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt
2.
Dipartimento di Matematica e Informatica, Università di Catania; RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russia

Received: 12 August 2022 Revised: 04 September 2022 Accepted: 14 September 2022 Published: 16 September 2022
MSC : 35J10, 35C08, 35A18, 34A08

In the existing article, the existence of solutions to nonlinear fractional differential inclusions in the sense of the Atangana-Baleanu-Caputo ($ \mathcal{ABC} $) fractional derivatives in Banach space is studied. The investigation of the main results relies on the set-valued issue of Mönch fixed point theorem incorporated with the Kuratowski measure of non-compactness. A simulated example is proposed to explain the obtained results.
- Atangana-Baleanu fractional derivatives,
- measure of non-compactness,
- Mönch fixed point theorem
Citation: Mohamed I. Abbas, Maria Alessandra Ragusa. Nonlinear fractional differential inclusions with non-singular Mittag-Leffler kernel[J]. AIMS Mathematics, 2022, 7(11): 20328-20340. doi: 10.3934/math.20221113

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Abstract

In the existing article, the existence of solutions to nonlinear fractional differential inclusions in the sense of the Atangana-Baleanu-Caputo ($ \mathcal{ABC} $) fractional derivatives in Banach space is studied. The investigation of the main results relies on the set-valued issue of Mönch fixed point theorem incorporated with the Kuratowski measure of non-compactness. A simulated example is proposed to explain the obtained results.

References

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