Solution of differential equations with infinite delay via coupled fixed point
K Mebarki1,2, A Boudaoui1,2, W Shatanawi3,4,5
1Department of Mathematics and Computer Science, University of Adrar, Algeria.
Heliyon
|February 10, 2022
Summary
This study unifies fixed point theorems in graph-enriched metric spaces. These findings establish new conditions for solving differential equations with infinite delays.
Area of Science:
- Mathematics
- Applied Mathematics
- Functional Analysis
Background:
- Fixed-point theory is crucial for solving equations in various mathematical fields.
- Metric spaces endowed with graphs offer a generalized framework for fixed-point problems.
- Differential equations with infinite delay present significant theoretical and practical challenges.
Purpose of the Study:
- To unify and generalize existing fixed-point results in the context of metric spaces with graphs.
- To develop novel sufficient conditions for the existence of solutions to differential equations with infinite delay.
Main Methods:
- Utilizing concepts from graph theory and metric spaces.
- Developing and applying novel fixed-point theorems.
- Establishing existence criteria for solutions of functional differential equations.
Main Results:
- A unified and generalized set of fixed-point theorems for graph-enriched metric spaces.
- New sufficient conditions for guaranteeing the existence of solutions for differential equations with infinite delay.
Conclusions:
- The presented fixed-point theorems offer a broader applicability than previous results.
- The study contributes to the theory of differential equations with infinite delay by providing new existence conditions.
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