Existence and stability results for impulsive $ (k, \psi) $-Hilfer fractional double integro-differential equation with mixed nonlocal conditions

Weerawat Sudsutad; Wicharn Lewkeeratiyutkul; Chatthai Thaiprayoon; Jutarat Kongson; Weerawat Sudsutad; Wicharn Lewkeeratiyutkul; Chatthai Thaiprayoon; Jutarat Kongson

doi:10.3934/math.20231042

AIMS Mathematics

2023, Volume 8, Issue 9: 20437-20476. doi: 10.3934/math.20231042

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Research article Special Issues

Existence and stability results for impulsive $ (k, \psi) $-Hilfer fractional double integro-differential equation with mixed nonlocal conditions

1.
Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
2.
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, 10330, Bangkok, Thailand
3.
Research Group of Theoretical and Computational Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand

Received: 12 May 2023 Revised: 13 June 2023 Accepted: 14 June 2023 Published: 25 June 2023
MSC : 26A33, 33E12, 34A37, 34B10, 34D20

This paper investigates a class of nonlinear impulsive fractional integro-differential equations with mixed nonlocal boundary conditions (multi-point and multi-term) that involves $ (\rho_{k}, \psi_{k}) $-Hilfer fractional derivative. The main objective is to prove the existence and uniqueness of the solution for the considered problem by means of fixed point theory of Banach's and O'Regan's types, respectively. In this contribution, the transformation of the considered problem into an equivalent integral equation is necessary for our main results. Furthermore, the nonlinear functional analysis technique is used to investigate various types of Ulam's stability results. The applications of main results are guaranteed with three numerical examples.
- $ (k, \psi) $-Hilfer fractional derivative,
- impulsive conditions,
- nonlocal conditions,
- fixed-point theorems,
- Ulam stability
Citation: Weerawat Sudsutad, Wicharn Lewkeeratiyutkul, Chatthai Thaiprayoon, Jutarat Kongson. Existence and stability results for impulsive $ (k, \psi) $-Hilfer fractional double integro-differential equation with mixed nonlocal conditions[J]. AIMS Mathematics, 2023, 8(9): 20437-20476. doi: 10.3934/math.20231042

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Abstract

This paper investigates a class of nonlinear impulsive fractional integro-differential equations with mixed nonlocal boundary conditions (multi-point and multi-term) that involves $ (\rho_{k}, \psi_{k}) $-Hilfer fractional derivative. The main objective is to prove the existence and uniqueness of the solution for the considered problem by means of fixed point theory of Banach's and O'Regan's types, respectively. In this contribution, the transformation of the considered problem into an equivalent integral equation is necessary for our main results. Furthermore, the nonlinear functional analysis technique is used to investigate various types of Ulam's stability results. The applications of main results are guaranteed with three numerical examples.

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