Existence results for nonlinear multi-term impulsive fractional $ q $-integro-difference equations with nonlocal boundary conditions

Ravi P. Agarwal; Bashir Ahmad; Hana Al-Hutami; Ahmed Alsaedi; Ravi P. Agarwal; Bashir Ahmad; Hana Al-Hutami; Ahmed Alsaedi

doi:10.3934/math.2023985

AIMS Mathematics

2023, Volume 8, Issue 8: 19313-19333. doi: 10.3934/math.2023985

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Existence results for nonlinear multi-term impulsive fractional $ q $-integro-difference equations with nonlocal boundary conditions

1.
Department of Mathematics, Texas A & M University, Kingsville, Texas 78363-8202, USA
2.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 15 March 2023 Revised: 20 May 2023 Accepted: 04 June 2023 Published: 08 June 2023
MSC : 34A08, 39A13, 34B15, 34B37

This paper is concerned with the existence of solutions for a nonlinear multi-term impulsive fractional $ q $-integro-difference equation with nonlocal boundary conditions. The appropriated fixed point theorems are applied to accomplish the existence and uniqueness results for the given problem. We demonstrate the application of the obtained results with the aid of examples.
- fractional $ q $-derivative operator,
- Riemann-Liouville fractional $ q $-integral operator,
- impulse,
- nonlocal boundary conditions,
- existence of a solution
Citation: Ravi P. Agarwal, Bashir Ahmad, Hana Al-Hutami, Ahmed Alsaedi. Existence results for nonlinear multi-term impulsive fractional $ q $-integro-difference equations with nonlocal boundary conditions[J]. AIMS Mathematics, 2023, 8(8): 19313-19333. doi: 10.3934/math.2023985

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Abstract

This paper is concerned with the existence of solutions for a nonlinear multi-term impulsive fractional $ q $-integro-difference equation with nonlocal boundary conditions. The appropriated fixed point theorems are applied to accomplish the existence and uniqueness results for the given problem. We demonstrate the application of the obtained results with the aid of examples.

References

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