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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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02089-5 |
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| author | Kanagaraj Muthuselvan Nachiappan Nithya Fahad Aljuaydi Kottakkaran Sooppy Nisar |
| author_facet | Kanagaraj Muthuselvan Nachiappan Nithya Fahad Aljuaydi Kottakkaran Sooppy Nisar |
| author_sort | Kanagaraj Muthuselvan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1c191994df8e490ea631135266f7648c |
| institution | DOAJ |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-1c191994df8e490ea631135266f7648c2025-08-20T03:03:44ZengSpringerOpenBoundary Value Problems1687-27702025-07-012025111910.1186/s13661-025-02089-5A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet methodKanagaraj Muthuselvan0Nachiappan Nithya1Fahad Aljuaydi2Kottakkaran Sooppy Nisar3Department of Mathematics, Amrita School of Engineering, Amrita Vishwa VidyapeethamDepartment of Mathematics, Thiagarajar College of EngineeringDepartment of Mathematics, College of Science and Humanities in Al Kharj, Prince Sattam bin Abdulaziz UniversityDepartment of Mathematics, College of Science and Humanities in Al Kharj, Prince Sattam bin Abdulaziz UniversityAbstract 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.https://doi.org/10.1186/s13661-025-02089-5Hilfer fractional derivativesConstant delayConvergence analysisError analysis |
| spellingShingle | Kanagaraj Muthuselvan Nachiappan Nithya Fahad Aljuaydi Kottakkaran Sooppy Nisar A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method Boundary Value Problems Hilfer fractional derivatives Constant delay Convergence analysis Error analysis |
| title | A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method |
| title_full | A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method |
| title_fullStr | A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method |
| title_full_unstemmed | A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method |
| title_short | A numerical technique for solving neutral Hilfer fractional differential equation with constant delay using Legendre wavelet method |
| title_sort | numerical technique for solving neutral hilfer fractional differential equation with constant delay using legendre wavelet method |
| topic | Hilfer fractional derivatives Constant delay Convergence analysis Error analysis |
| url | https://doi.org/10.1186/s13661-025-02089-5 |
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