Solution of differential equations with infinite delay via coupled fixed point

K Mebarki; A Boudaoui; W Shatanawi; K Abodayeh; Taqi A M Shatnawi

doi:10.1016/j.heliyon.2022.e08849

Solution of differential equations with infinite delay via coupled fixed point

Heliyon. 2022 Jan 31;8(2):e08849. doi: 10.1016/j.heliyon.2022.e08849. eCollection 2022 Feb.

Authors

K Mebarki^{1

2}, A Boudaoui^{1

2}, W Shatanawi^{3

4

5}, K Abodayeh³, Taqi A M Shatnawi⁵

Affiliations

¹ Department of Mathematics and Computer Science, University of Adrar, Algeria.
² Laboratory of Mathematics Modeling and Applications, University of Adrar, National Road No. 06, 01000, Adrar, Algeria.
³ Department of General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
⁴ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan.
⁵ Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan.

Abstract

This manuscript aims to prove exciting results that unify and generalize several fixed point results for metric spaces endowed with graphs. As an application, we apply our own results to give and introduce sufficient conditions to guarantee existence solutions of such differential equations with infinite delay.

Keywords: Couple fixed point; Directed graph; Mixed G-monotone; b-metric space.