On a set-valued functional integral equation of Volterra-Stieltjes type

Volume 21, Issue 4, pp 273--285 http://dx.doi.org/10.22436/jmcs.021.04.01

Publication Date: April 29, 2020 Submission Date: March 08, 2020 Revision Date: March 15, 2020 Accteptance Date: April 08, 2020

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Authors

A. M. A. El-Sayed - Faculty of Science , Alexandria University, Alexandria, Egypt. Sh. M. Al-Issa - Faculty of Science, Lebanes International University, Beirut, Lebanon. - Faculty of Science, The International University of Beirut, Saida, Lebanon.

Abstract

In this paper, we study the existence of continuous solutions of a set-valued functional integral equation for the Volterra-Stieltjes type. The asymptotic stability of the solutions will be studied. The continuous dependence of the solution on the set of selections of the set-valued function will be proven. As an application, we study the existence of solutions of an initial value problem of arbitrary (fractional) order differential inclusion.

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Keywords

• Nonlinear Volterra-Stieltjes integral inclusion
• function of bounded variation
• asymptotic stability
• continuous dependence of the solution
• integral inclusion of fractional order

MSC

•  74H10
•  45G10

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