A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method

A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method

Abstract This study aims to explore the Legendre wavelet method for numerically solving neutral fractional differential equations with constant delay using fractional derivatives in the Hilfer sense. By utilizing the function approximation and properties of the Legendre wavelet, we derive an approxi...

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Bibliographic Details
Main Authors: Kanagaraj Muthuselvan, Nachiappan Nithya, Fahad Aljuaydi, Kottakkaran Sooppy Nisar
Format: Article
Language:English
Published: SpringerOpen 2025-07-01
Series:Boundary Value Problems
Subjects:
Hilfer fractional derivatives
Constant delay
Convergence analysis
Error analysis
Online Access:https://doi.org/10.1186/s13661-025-02089-5
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Summary:Abstract This study aims to explore the Legendre wavelet method for numerically solving neutral fractional differential equations with constant delay using fractional derivatives in the Hilfer sense. By utilizing the function approximation and properties of the Legendre wavelet, we derive an approximate solution for the given dynamical system, reducing the neutral Hilfer fractional derivatives with constant delay to algebraic expressions. Additionally, we present a convergence analysis and error estimation for the truncated Legendre wavelet expansion in the context of the proposed method. To verify the effectiveness of the approach, several numerical examples are provided, along with graphical illustrations that clearly demonstrate the applicability and accuracy of the method, thereby supporting the validity of the theoretical results.
ISSN:1687-2770

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