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On the nonlinear Hadamard-type integro-differential equation
1Department of Mathematics and Computer Science, Brandon University, Brandon, Manitoba R7A 6A9 Canada.
Fixed Point Theory and Algorithms for Sciences and Engineering
|April 8, 2021
Summary
This study proves the unique solution for a nonlinear Hadamard-type integro-differential equation using Babenko
Area of Science:
- Mathematics
- Applied Mathematics
- Differential Equations
Background:
- Integro-differential equations are crucial in modeling complex systems.
- Nonlinear equations present significant analytical challenges.
- Hadamard-type operators introduce specific properties requiring tailored methods.
Purpose of the Study:
- To establish the uniqueness of solutions for a specific class of nonlinear Hadamard-type integro-differential equations.
- To extend existing analytical techniques to a more complex equation type.
- To provide a rigorous mathematical framework for analyzing such equations.
Main Methods:
- Utilizing Babenko's approach for analyzing functional equations.
- Applying Banach's contraction principle to demonstrate solution uniqueness.
- Working within the Banach space of absolutely continuous functions.
Main Results:
- The paper establishes the conditions under which a unique solution exists.
- The theoretical findings are demonstrated through two practical examples.
- The study confirms the applicability of the employed methods.
Conclusions:
- The research successfully demonstrates the uniqueness of solutions for the studied equation.
- The findings contribute to the theoretical understanding of nonlinear integro-differential equations.
- The provided examples validate the developed methodology.
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