A Computational Method for Solving Nonlinear Fractional Integral Equations

This article solves the nonlinear fractional integral equation (NFrIE) using the Genocchi polynomial method (GPM). We have provided proof to demonstrate the existence of a unique solution to the second sort of NFrIE in Hilbert space. The proof of the stability of the error has been described and dis...

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Bibliographic Details
Published in:Fractal and fractional 2024-11, Vol.8 (11), p.663
Main Authors: Matoog, Rajaa T., Mahdy, Amr M. S., Abdou, Mohamed A., Mohamed, Doaa Sh
Format: Article
Language:English
Subjects:
existence and uniqueness
Fractional calculus
Genocchi polynomial method
Hilbert space
Integral equations
Mathematical analysis
nonlinear fractional integral equation
Operators (mathematics)
Polynomials
self adjoint operator
spectrum relations
Stability criteria
stability of error
Uniqueness
Citations: Items that this one cites
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Summary:This article solves the nonlinear fractional integral equation (NFrIE) using the Genocchi polynomial method (GPM). We have provided proof to demonstrate the existence of a unique solution to the second sort of NFrIE in Hilbert space. The proof of the stability of the error has been described and discussed. These criteria are proven given the spectrum characteristics of a linear self-adjoint operator. Numerous applications, unique conditions, and specific situations are developed. Additionally, numerical examples are constructed to illustrate the efficiency and applicability of the method. Maple 18 software is utilized for the computation of all the numerical outcomes.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8110663