Investigation of Caputo proportional fractional integro-differential equation with mixed nonlocal conditions with respect to another function

Bounmy Khaminsou; Weerawat Sudsutad; Jutarat Kongson; Somsiri Nontasawatsri; Adirek Vajrapatkul; Chatthai Thaiprayoon; Bounmy Khaminsou; Weerawat Sudsutad; Jutarat Kongson; Somsiri Nontasawatsri; Adirek Vajrapatkul; Chatthai Thaiprayoon

doi:10.3934/math.2022531

AIMS Mathematics

2022, Volume 7, Issue 6: 9549-9576. doi: 10.3934/math.2022531

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Research article

Investigation of Caputo proportional fractional integro-differential equation with mixed nonlocal conditions with respect to another function

1.
Department of Mathematics and Statistics, Faculty of Natural Science, National University of Laos, 01080, Laos
2.
Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
3.
Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
4.
Center of Excellence in Mathematics, CHE, Sri Ayutthaya Rd., Bangkok 10400, Thailand
5.
Department of Health Technology, Faculty of Science and Health Technology, Navamindradhiraj University, Bangkok 10300, Thailand
6.
School of Economics, Sukhothai Thammathirat Open University, Chaengwattana Road, Bangpood, Pakkret, Nonthaburi 11120, Thailand

Received: 27 December 2021 Revised: 26 February 2022 Accepted: 28 February 2022 Published: 14 March 2022
MSC : 26A33, 34A08, 34B10, 34D20

In this manuscript, we analyze the existence, uniqueness and Ulam's stability for Caputo proportional fractional integro-differential equation involving mixed nonlocal conditions with respect to another function. The uniqueness result is proved via Banach's fixed point theorem and the existence results are established by using the Leray-Schauder nonlinear alternative and Krasnoselskii's fixed point theorem. Furthermore, by using the nonlinear analysis techniques, we investigate appropriate conditions and results to study various different types of Ulam's stability. In addition, numerical examples are also constructed to demonstrate the application of the main results.
- existence and uniqueness,
- fractional differential equations,
- fixed point theorems,
- Ulam's stability,
- nonlocal conditions
Citation: Bounmy Khaminsou, Weerawat Sudsutad, Jutarat Kongson, Somsiri Nontasawatsri, Adirek Vajrapatkul, Chatthai Thaiprayoon. Investigation of Caputo proportional fractional integro-differential equation with mixed nonlocal conditions with respect to another function[J]. AIMS Mathematics, 2022, 7(6): 9549-9576. doi: 10.3934/math.2022531

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Abstract

In this manuscript, we analyze the existence, uniqueness and Ulam's stability for Caputo proportional fractional integro-differential equation involving mixed nonlocal conditions with respect to another function. The uniqueness result is proved via Banach's fixed point theorem and the existence results are established by using the Leray-Schauder nonlinear alternative and Krasnoselskii's fixed point theorem. Furthermore, by using the nonlinear analysis techniques, we investigate appropriate conditions and results to study various different types of Ulam's stability. In addition, numerical examples are also constructed to demonstrate the application of the main results.

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