Fractional-order boundary value problems solutions using advanced numerical technique
The main motivation of this study is to extend the use of the operational matrices approach to solve fractional-order two-point boundary value problems (TPBVPs), a method often employed in the literature for solving fractional-order initial value problems. Our proposed approach employs innovative op...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124004455 |
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| author | Asmat Batool Imran Talib Muhammad Bilal Riaz |
| author_facet | Asmat Batool Imran Talib Muhammad Bilal Riaz |
| author_sort | Asmat Batool |
| collection | DOAJ |
| description | The main motivation of this study is to extend the use of the operational matrices approach to solve fractional-order two-point boundary value problems (TPBVPs), a method often employed in the literature for solving fractional-order initial value problems. Our proposed approach employs innovative operational matrices, specifically the integral operational matrices based on Chelyshkov polynomials (CPs), a type of orthogonal polynomials. These operational matrices enable us to integrate monomial terms into the algorithm, effectively converting the problem into easily solvable Sylvester-type equations. We provide a comprehensive comparison to demonstrate the accuracy and computational advantages of our proposed approach against existing methods, including the exact solution, the Haar wavelet method (HWM), the Bessel collocation method (BCM), the Pseudo Spectral Method (PSM), the Generalized Adams–Bashforth–Moulton Method (GABMM) and the fractional central difference scheme (FCDS) through numerical examples. Additionally, our proposed approach is well-suited for solving problems with both polynomial and non-polynomial solutions. |
| format | Article |
| id | doaj-art-af9be471c1a24f69a0671250a98fb434 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-af9be471c1a24f69a0671250a98fb4342025-01-08T04:53:46ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101059Fractional-order boundary value problems solutions using advanced numerical techniqueAsmat Batool0Imran Talib1Muhammad Bilal Riaz2Department of Mathematics, University of Management and Technology, Lahore, PakistanNonlinear Analysis Group, Department of Mathematics, Virtual University of Pakistan, Lahore, Pakistan; Corresponding author.Department of Mathematics, University of Management and Technology, Lahore, Pakistan; IT4Innovations, VSB – Technical University of Ostrava, Ostrava, Czech RepublicThe main motivation of this study is to extend the use of the operational matrices approach to solve fractional-order two-point boundary value problems (TPBVPs), a method often employed in the literature for solving fractional-order initial value problems. Our proposed approach employs innovative operational matrices, specifically the integral operational matrices based on Chelyshkov polynomials (CPs), a type of orthogonal polynomials. These operational matrices enable us to integrate monomial terms into the algorithm, effectively converting the problem into easily solvable Sylvester-type equations. We provide a comprehensive comparison to demonstrate the accuracy and computational advantages of our proposed approach against existing methods, including the exact solution, the Haar wavelet method (HWM), the Bessel collocation method (BCM), the Pseudo Spectral Method (PSM), the Generalized Adams–Bashforth–Moulton Method (GABMM) and the fractional central difference scheme (FCDS) through numerical examples. Additionally, our proposed approach is well-suited for solving problems with both polynomial and non-polynomial solutions.http://www.sciencedirect.com/science/article/pii/S2666818124004455Chelyshkov polynomialsCaputo fractional derivativeTwo-point boundary value problemsFractional differential equationsOperational matrices approachOrthogonal polynomials |
| spellingShingle | Asmat Batool Imran Talib Muhammad Bilal Riaz Fractional-order boundary value problems solutions using advanced numerical technique Partial Differential Equations in Applied Mathematics Chelyshkov polynomials Caputo fractional derivative Two-point boundary value problems Fractional differential equations Operational matrices approach Orthogonal polynomials |
| title | Fractional-order boundary value problems solutions using advanced numerical technique |
| title_full | Fractional-order boundary value problems solutions using advanced numerical technique |
| title_fullStr | Fractional-order boundary value problems solutions using advanced numerical technique |
| title_full_unstemmed | Fractional-order boundary value problems solutions using advanced numerical technique |
| title_short | Fractional-order boundary value problems solutions using advanced numerical technique |
| title_sort | fractional order boundary value problems solutions using advanced numerical technique |
| topic | Chelyshkov polynomials Caputo fractional derivative Two-point boundary value problems Fractional differential equations Operational matrices approach Orthogonal polynomials |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124004455 |
| work_keys_str_mv | AT asmatbatool fractionalorderboundaryvalueproblemssolutionsusingadvancednumericaltechnique AT imrantalib fractionalorderboundaryvalueproblemssolutionsusingadvancednumericaltechnique AT muhammadbilalriaz fractionalorderboundaryvalueproblemssolutionsusingadvancednumericaltechnique |