Study of multi term delay fractional order impulsive differential equation using fixed point approach

Amjad Ali; Kamal Shah; Dildar Ahmad; Ghaus Ur Rahman; Nabil Mlaiki; Thabet Abdeljawad; Amjad Ali; Kamal Shah; Dildar Ahmad; Ghaus Ur Rahman; Nabil Mlaiki; Thabet Abdeljawad

doi:10.3934/math.2022644

AIMS Mathematics

2022, Volume 7, Issue 7: 11551-11580. doi: 10.3934/math.2022644

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Study of multi term delay fractional order impulsive differential equation using fixed point approach

1.
Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11585, Saudi Arabia
3.
Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 08 November 2021 Revised: 21 March 2022 Accepted: 28 March 2022 Published: 14 April 2022
MSC : 26A33, 34A08

This manuscript is devoted to investigate a class of multi terms delay fractional order impulsive differential equations. Our investigation includes existence theory along with Ulam type stability. By using classical fixed point theorems, we establish sufficient conditions for existence and uniqueness of solution to the proposed problem. We develop some appropriate conditions for different kinds of Ulam-Hyers stability results by using tools of nonlinear functional analysis. We demonstrate our results by an example.
- impulsive delay differential equations,
- existence theory,
- Banach theorem,
- stability analysis
Citation: Amjad Ali, Kamal Shah, Dildar Ahmad, Ghaus Ur Rahman, Nabil Mlaiki, Thabet Abdeljawad. Study of multi term delay fractional order impulsive differential equation using fixed point approach[J]. AIMS Mathematics, 2022, 7(7): 11551-11580. doi: 10.3934/math.2022644

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Abstract

This manuscript is devoted to investigate a class of multi terms delay fractional order impulsive differential equations. Our investigation includes existence theory along with Ulam type stability. By using classical fixed point theorems, we establish sufficient conditions for existence and uniqueness of solution to the proposed problem. We develop some appropriate conditions for different kinds of Ulam-Hyers stability results by using tools of nonlinear functional analysis. We demonstrate our results by an example.

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