Existence results of mild solutions for nonlocal fractional delay integro-differential evolution equations via Caputo conformable fractional derivative

Lahcene Rabhi; Mohammed Al Horani; Roshdi Khalil; Lahcene Rabhi; Mohammed Al Horani; Roshdi Khalil

doi:10.3934/math.2022647

AIMS Mathematics

2022, Volume 7, Issue 7: 11614-11634. doi: 10.3934/math.2022647

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Research article

Existence results of mild solutions for nonlocal fractional delay integro-differential evolution equations via Caputo conformable fractional derivative

1.
Laboratory of Geometry, Analysis, Control and Applications, Dr Moulay Tahar University of Saida, B. P. 138, En-nasr, 20000 Saida, Algeria
2.
Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

Received: 07 February 2022 Revised: 15 March 2022 Accepted: 28 March 2022 Published: 14 April 2022
MSC : 34G10, 26A33

In this paper, we investigate the existence of mild solutions for nonlocal delay fractional Cauchy problem with Caputo conformable derivative in Banach spaces. We establish a representation of a mild solution using a fractional Laplace transform. The existence of such solutions is proved under certain conditions, using the Mönch fixed point theorem and a general version of Gronwall's inequality under weaker conditions in the sense of Kuratowski measure of non compactness. Applications illustrating our main abstract results and showing the applicability of the presented theory are also given.
- fractional Laplace transform,
- nonlocal delay fractional evolution equation,
- mild solution,
- Mönch's fixed point theorem
Citation: Lahcene Rabhi, Mohammed Al Horani, Roshdi Khalil. Existence results of mild solutions for nonlocal fractional delay integro-differential evolution equations via Caputo conformable fractional derivative[J]. AIMS Mathematics, 2022, 7(7): 11614-11634. doi: 10.3934/math.2022647

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Abstract

In this paper, we investigate the existence of mild solutions for nonlocal delay fractional Cauchy problem with Caputo conformable derivative in Banach spaces. We establish a representation of a mild solution using a fractional Laplace transform. The existence of such solutions is proved under certain conditions, using the Mönch fixed point theorem and a general version of Gronwall's inequality under weaker conditions in the sense of Kuratowski measure of non compactness. Applications illustrating our main abstract results and showing the applicability of the presented theory are also given.

References

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