On coupled impulsive fractional integro-differential equations with Riemann-Liouville derivatives

Xiaoming Wang; Mehboob Alam; Akbar Zada; Xiaoming Wang; Mehboob Alam; Akbar Zada

doi:10.3934/math.2021094

AIMS Mathematics

2021, Volume 6, Issue 2: 1561-1595. doi: 10.3934/math.2021094

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Research article

On coupled impulsive fractional integro-differential equations with Riemann-Liouville derivatives

1.
School of Mathematics & Computer Science, Shangrao Normal University, Shangrao 334001, China
2.
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan

Received: 08 October 2020 Accepted: 16 November 2020 Published: 24 November 2020
MSC : 26A33, 34A08, 34B27

In this paper, we investigate the existence, uniqueness and stability of coupled impulsive fractional integro-differential equations with Riemann-Liouville derivatives. To prove the existence and uniqueness results for afore mentioned system, we use the techniques of Kransnoselskiios type fixed point theorem. Furthermore, different kinds of Ulam stabilities are discussed along with examples, to demonstrate the validity of main results.
- Riemann-Liouville fractional derivatives,
- fractional integro-differential equations,
- coupled system,
- impulses,
- Ulam stability
Citation: Xiaoming Wang, Mehboob Alam, Akbar Zada. On coupled impulsive fractional integro-differential equations with Riemann-Liouville derivatives[J]. AIMS Mathematics, 2021, 6(2): 1561-1595. doi: 10.3934/math.2021094

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Abstract

In this paper, we investigate the existence, uniqueness and stability of coupled impulsive fractional integro-differential equations with Riemann-Liouville derivatives. To prove the existence and uniqueness results for afore mentioned system, we use the techniques of Kransnoselskiios type fixed point theorem. Furthermore, different kinds of Ulam stabilities are discussed along with examples, to demonstrate the validity of main results.

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