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Uniqueness of the Hadamard-type integral equations
1Department of Mathematics and Computer Science, Brandon University, Brandon, Manitoba R7A 6A9 Canada.
Advances in Difference Equations
|January 22, 2021
Summary
This study explores the uniqueness of solutions for Hadamard-type integral equations within Banach spaces. New findings leverage Babenko
Area of Science:
- Mathematical Analysis
- Functional Analysis
- Integral Equations
Background:
- Integral equations are fundamental in various scientific and engineering fields.
- Banach spaces provide a powerful framework for studying solutions to equations.
- Uniqueness of solutions is crucial for the well-posedness of mathematical models.
Purpose of the Study:
- To investigate the uniqueness of solutions for Hadamard-type integral equations.
- To analyze a related coupled system of integral equations.
- To extend existing methods for solution uniqueness in Banach spaces.
Main Methods:
- Application of Babenko's approach.
- Utilization of Banach's contraction principle.
- Analysis of integral equations in the context of Banach spaces.
Main Results:
- Established new theorems regarding the uniqueness of solutions.
- Demonstrated the applicability of the methods to a coupled system.
- Provided illustrative examples to support the theoretical findings.
Conclusions:
- The study contributes novel results to the theory of integral equations.
- The employed methods offer a robust framework for uniqueness analysis.
- Further research can explore extensions to different types of equations or spaces.
Keywords:
Babenko’s approachBanach’s fixed point theoremHadamard-type integralMultivariate Mittag-Leffler functionMore Related Videos
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