Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative

Thanin Sitthiwirattham; Rozi Gul; Kamal Shah; Ibrahim Mahariq; Jarunee Soontharanon; Khursheed J. Ansari; Thanin Sitthiwirattham; Rozi Gul; Kamal Shah; Ibrahim Mahariq; Jarunee Soontharanon; Khursheed J. Ansari

doi:10.3934/math.2022222

AIMS Mathematics

2022, Volume 7, Issue 3: 4017-4037. doi: 10.3934/math.2022222

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Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative

1.
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand
2.
Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan
3.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
4.
College of Engineering and Technology, American University of the Middle East, Kuwait
5.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
6.
Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia

Received: 25 October 2021 Accepted: 02 December 2021 Published: 13 December 2021
MSC : 26A33, 34A08

This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.
- Caputo-Fabrizio fractional derivative,
- stability results,
- fixed point results,
- g-H-U stability
Citation: Thanin Sitthiwirattham, Rozi Gul, Kamal Shah, Ibrahim Mahariq, Jarunee Soontharanon, Khursheed J. Ansari. Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative[J]. AIMS Mathematics, 2022, 7(3): 4017-4037. doi: 10.3934/math.2022222

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Abstract

This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.

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