Investigation of Caputo proportional fractional integro-differential equation with mixed nonlocal conditions with respect to another function-Reference-Cited by-同舟云学术

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

Published:2022 Issue:6 Volume:7 Page:9549-9576
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Khaminsou Bounmy¹,Sudsutad Weerawat²,Kongson Jutarat³⁴,Nontasawatsri Somsiri⁵,Vajrapatkul Adirek⁶,Thaiprayoon Chatthai³⁴

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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