A study on the existence results of boundary value problems of fractional relaxation integro-differential equations with impulsive and delay conditions in Banach spaces-Reference-Cited by-同舟云学术

A study on the existence results of boundary value problems of fractional relaxation integro-differential equations with impulsive and delay conditions in Banach spaces

Published:2024 Issue:5 Volume:9 Page:11468-11485
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Chasreechai Saowaluck¹²,Poornima Sadhasivam³,Karthikeyann Panjaiyan³,Karthikeyan Kulandhaivel⁴,Kumar Anoop⁵,Kaushik Kirti⁵,Sitthiwirattham Thanin²⁶

Affiliation:

1. Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

2. Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

3. Department of Mathematics, Sri Vasavi College, Erode 638136, India

4. Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641407, Tamil Nadu, India

5. Department of Mathematics and Statistics, Central Univeristy of Punjab, Bathinda, Punjab, India

6. Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand

Abstract

<abstract><p>The aim of this paper was to provide systematic approaches to study the existence of results for the system fractional relaxation integro-differential equations. Applied problems require definitions of fractional derivatives, allowing the utilization of physically interpretable boundary conditions. Impulsive conditions serve as basic conditions to study the dynamic processes that are subject to sudden changes in their state. In the process, we converted the given fractional differential equations into an equivalent integral equation. We constructed appropriate mappings and employed the Schaefer's fixed-point theorem and the Banach fixed-point theorem to show the existence of a unique solution. We presented an example to show the applicability of our results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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