A study on controllability for Hilfer fractional differential equations with impulsive delay conditions

Kulandhaivel Karthikeyan; Palanisamy Raja Sekar; Panjaiyan Karthikeyan; Anoop Kumar; Thongchai Botmart; Wajaree Weera; Kulandhaivel Karthikeyan; Palanisamy Raja Sekar; Panjaiyan Karthikeyan; Anoop Kumar; Thongchai Botmart; Wajaree Weera

doi:10.3934/math.2023209

AIMS Mathematics

2023, Volume 8, Issue 2: 4202-4219. doi: 10.3934/math.2023209

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Research article

A study on controllability for Hilfer fractional differential equations with impulsive delay conditions

1.
Department of Mathematics, Center for Research and Development, KPR Institute of Engineering and Technology, Coimbatore, Tamilnadu, India
2.
Department of Mathematics, K.S.R College of Engineering, Tiruchengode, Namakkal, Tamilnadu, India
3.
Department of Mathematics, Sri Vasavi College, Erode, Tamilnadu, India
4.
Department of Mathematics and Statistics, School of Basic Sciences, Central University of Punjab, VPO-Ghudda, Bathinda, Punjab 151401, India
5.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 25 September 2022 Revised: 09 November 2022 Accepted: 13 November 2022 Published: 02 December 2022
MSC : 93B05, 34K30, 34K40, 47H08, 47H10

This article focuses on the controllability of a Hilfer fractional impulsive differential equation with indefinite delay. We analyze our major outcomes using fractional calculus, the measure of non-compactness and a fixed-point approach. Finally, an example is provided to show the theory.
- boundary condition,
- fractional calculus,
- implusive condition,
- integro-differential system,
- controllability,
- fixed-point theorem
Citation: Kulandhaivel Karthikeyan, Palanisamy Raja Sekar, Panjaiyan Karthikeyan, Anoop Kumar, Thongchai Botmart, Wajaree Weera. A study on controllability for Hilfer fractional differential equations with impulsive delay conditions[J]. AIMS Mathematics, 2023, 8(2): 4202-4219. doi: 10.3934/math.2023209

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Abstract

This article focuses on the controllability of a Hilfer fractional impulsive differential equation with indefinite delay. We analyze our major outcomes using fractional calculus, the measure of non-compactness and a fixed-point approach. Finally, an example is provided to show the theory.

References

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