On the existence and stability of Caputo Volterra-Fredholm systems

Volume 30, Issue 4, pp 322--331 http://dx.doi.org/10.22436/jmcs.030.04.02

Publication Date: February 09, 2023 Submission Date: October 15, 2022 Revision Date: December 12, 2022 Accteptance Date: December 31, 2022

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Authors

S. A. M. Jameel - Department of Computer Systems, Middle Technical University, Institute of Administration Rusafa, Baghdad-10045, Iraq.

Abstract

In this paper, we discuss several problems related to the neutral fractional Volterra-Fredholm integro-differential systems in Banach spaces. Existence of the Schaefer's fixed point and Ulam-Hyers-Rassias stability properties for the fixed point problem will be discussed. Some results are presented, under appropriate conditions, and some open questions are pointed out. Our results extend recent results given for \(\psi\)-fractional derivative.

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Keywords

• \(\psi\)-Caputo fractional derivative
• integro-differential equation
• fixed point technique
• stability problem

MSC

•  26A33
•  45J05
•  74H55