Characteristics of solutions of nonlinear neutral integro-differential equation via Chandrasekhar integral

Volume 24, Issue 2, pp 173--185 http://dx.doi.org/10.22436/jmcs.024.02.08

Publication Date: February 14, 2021 Submission Date: August 16, 2020 Revision Date: January 01, 2021 Accteptance Date: January 18, 2021

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Authors

H. H. G. Hashem - Faculty of Science, Alexandria University, Alexandria, Egypt. - Department of mathematics, College of Science, Qassim University, P.O. Box 6644, Buraidah 51452, Saudi Arabia. Hessah O. Alrashidi - Department of mathematics, College of Science, Qassim University, P.O. Box 6644, Buraidah 51452, Saudi Arabia.

Abstract

In this paper, we shall study the existence of at least one continuous solution for a nonlinear neutral differential equation via Chandrasekhar integral. Next, continuous dependence of the solution of that equation on the delay functions will be studied. Also, we use Kransnoselskii theorem to prove the existence of solutions and estimate upper and lower bounds for solutions defined in unbounded interval. Some particular cases and remarks are presented to illustrate our results.

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Keywords

• Neutral differential equation
• Kransnoselskii theorem
• continuous dependence
• estimate upper and lower bounds for solutions

MSC

•  34A40
•  34A12
•  34A99
•  45D05

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