\(q\)-fractional functional integro-differential equation with \(q\)-integral condition

Volume 29, Issue 2, pp 167--174 https://doi.org/10.22436/jmcs.029.02.06

Publication Date: October 20, 2022 Submission Date: March 16, 2022 Revision Date: June 28, 2022 Accteptance Date: August 17, 2022

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Authors

R. G. Ahmed - Faculty of Science, Al-Azhar University, Cairo 11884, Egypt. Sh. A. Abd El-Salam - Faculty of Sciences, Damanhour University, Damanhour 22511, Egypt. A. M. A. El-Sayed - Faculty of Science, Alexandria University, Alexandria 21544, Egypt.

Abstract

In this paper, we study the existence and the uniqueness of the solution of the non-local problems of \(q\)-fractional functional integro-differential equation with non-local \(q\)-integral condition. The continuous dependence of the solution will be studied. Two examples will be given to illustrate results.

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Keywords

• Functional equations
• existence of solutions
• continuous dependence
• \(q\)-calculus

MSC

•  34B18
•  34A30

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