Existence of solutions for the boundary value problem of non-instantaneous impulsive fractional differential equations with $ p $-Laplacian operator

Yiyun Li; Jingli Xie; Luping Mao; Yiyun Li; Jingli Xie; Luping Mao

doi:10.3934/math.2022968

AIMS Mathematics

2022, Volume 7, Issue 9: 17592-17602. doi: 10.3934/math.2022968

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Existence of solutions for the boundary value problem of non-instantaneous impulsive fractional differential equations with $ p $-Laplacian operator

College of Mathematics and Statistics, Jishou University, Jishou, Hunan 416000, China

Received: 04 May 2022 Revised: 22 July 2022 Accepted: 24 July 2022 Published: 29 July 2022
MSC : 34A08, 34B37

In this paper, we consider a boundary value problem of impulsive fractional differential equations with the nonlinear $ p $-Laplacian operator, where impulses are non-instantaneous. By converting the given problem into an equivalent integral form and applying the Schauder fixed point theorem, we obtain some sufficient conditions for the existence of solutions. An illustrative example is presented to demonstrate the validity of our results.
- fractional differential equations,
- non-instantaneous impulsive,
- $ p $-Laplacian operator,
- fixed point theorem
Citation: Yiyun Li, Jingli Xie, Luping Mao. Existence of solutions for the boundary value problem of non-instantaneous impulsive fractional differential equations with $ p $-Laplacian operator[J]. AIMS Mathematics, 2022, 7(9): 17592-17602. doi: 10.3934/math.2022968

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Abstract

In this paper, we consider a boundary value problem of impulsive fractional differential equations with the nonlinear $ p $-Laplacian operator, where impulses are non-instantaneous. By converting the given problem into an equivalent integral form and applying the Schauder fixed point theorem, we obtain some sufficient conditions for the existence of solutions. An illustrative example is presented to demonstrate the validity of our results.

References

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