Optical applications of a generalized fractional integro-differential equation with periodicity

Dumitru Baleanu; Rabha W. Ibrahim; Dumitru Baleanu; Rabha W. Ibrahim

doi:10.3934/math.2023604

AIMS Mathematics

2023, Volume 8, Issue 5: 11953-11972. doi: 10.3934/math.2023604

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Research article

Optical applications of a generalized fractional integro-differential equation with periodicity

Dumitru Baleanu ^1,2,3,
Rabha W. Ibrahim ^{4,5,6
,
,}

1.
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
2.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10 - Turkey
5.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
6.
Information and Communication Technology Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar, Iraq

Received: 09 October 2022 Revised: 13 March 2023 Accepted: 15 March 2023 Published: 20 March 2023
MSC : 34A37, 26A33

Impulsive is the affinity to do something without thinking. In this effort, we model a mathematical formula types integro-differential equation (I-DE) to describe this behavior. We investigate periodic boundary value issues in Banach spaces for fractional a class of I-DEs with non-quick impulses. We provide numerous sufficient conditions of the existence of mild outcomes for I-DE utilizing the measure of non-compactness, the method of resolving domestic, and the fixed point result. Lastly, we illustrate a set of examples, which is given to demonstrate the investigations key findings. Our findings are generated some recent works in this direction.
- fractional calculus,
- fractional differential equation,
- fractional integral operator,
- fractional differential operator
Citation: Dumitru Baleanu, Rabha W. Ibrahim. Optical applications of a generalized fractional integro-differential equation with periodicity[J]. AIMS Mathematics, 2023, 8(5): 11953-11972. doi: 10.3934/math.2023604

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Abstract

Impulsive is the affinity to do something without thinking. In this effort, we model a mathematical formula types integro-differential equation (I-DE) to describe this behavior. We investigate periodic boundary value issues in Banach spaces for fractional a class of I-DEs with non-quick impulses. We provide numerous sufficient conditions of the existence of mild outcomes for I-DE utilizing the measure of non-compactness, the method of resolving domestic, and the fixed point result. Lastly, we illustrate a set of examples, which is given to demonstrate the investigations key findings. Our findings are generated some recent works in this direction.

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