New generalized conformable fractional impulsive delay differential equations with some illustrative examples

Hua Wang; Tahir Ullah Khan; Muhammad Adil Khan; Sajid Iqbal; Hua Wang; Tahir Ullah Khan; Muhammad Adil Khan; Sajid Iqbal

doi:10.3934/math.2021472

AIMS Mathematics

2021, Volume 6, Issue 8: 8149-8172. doi: 10.3934/math.2021472

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Research article

New generalized conformable fractional impulsive delay differential equations with some illustrative examples

1.
School of Mathematics and Statistics Changsha University of Science and Technology, Changsha 410114, China
2.
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
3.
Higher Education Department, Directorate General of Commerce Education and Management Sciencs KP, Peshawar, Pakistan
4.
Department of Mathematics, Riphah International University, Faisalabad Campus, Satyana Road, Faisalabad, Pakistan

Received: 03 February 2021 Accepted: 17 May 2021 Published: 25 May 2021
MSC : 26D15

This article is concerned to develop a novel generalized class of fractional impulsive delay differential equations. These equations are defined using newly discovered generalized conformable fractional operators which unify various previously-defined operators into a single form. The successive approximation method is employed and a sufficient criterion for the existence and uniqueness of the solution is developed. For the sake of illustration, three examples are provided at the end of the main results.
- fractional impulsive delay differential equations,
- conformable operators,
- successive approximation method,
- Banach spaces
Citation: Hua Wang, Tahir Ullah Khan, Muhammad Adil Khan, Sajid Iqbal. New generalized conformable fractional impulsive delay differential equations with some illustrative examples[J]. AIMS Mathematics, 2021, 6(8): 8149-8172. doi: 10.3934/math.2021472

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Abstract

This article is concerned to develop a novel generalized class of fractional impulsive delay differential equations. These equations are defined using newly discovered generalized conformable fractional operators which unify various previously-defined operators into a single form. The successive approximation method is employed and a sufficient criterion for the existence and uniqueness of the solution is developed. For the sake of illustration, three examples are provided at the end of the main results.

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