An Improved Numerical Algorithm for Solving Multi-Order Fractional Differential Equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10259949" target="_blank" >RIV/61989100:27740/25:10259949 - isvavai.cz</a>
Result on the web
<a href="https://www.taylorfrancis.com/chapters/edit/10.1201/9781003638339-10/improved-numerical-algorithm-solving-multi-order-fractional-differential-equations-zulfiqar-ahamad-noor-imran-talib-muhammad-bilal-riaz" target="_blank" >https://www.taylorfrancis.com/chapters/edit/10.1201/9781003638339-10/improved-numerical-algorithm-solving-multi-order-fractional-differential-equations-zulfiqar-ahamad-noor-imran-talib-muhammad-bilal-riaz</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
An Improved Numerical Algorithm for Solving Multi-Order Fractional Differential Equations
Original language description
This chapter extends a highly efficient computing technique based on newly developed operational matrices involving fractional integral and derivative operators of Vieta-Lucas function vectors (VLFVs). In contrast to the spectral collocation approach, our method does not depend on specific collocation point choices for solving fractional differential equations (FDEs). Additionally, it eliminates the need to expand residual functions as orthogonal polynomial series, a requirement in the spectral Tau method. Consequently, our proposed method demonstrates superior efficiency when compared to other methods documented in existing literature. Notably, we introduce a novel integral operational matrix for the Vieta-Lucas polynomial in the Riemann-Liouville context as a significant contribution to this work. Our computational approach facilitates the conversion of 325FDEs into a system of Sylvester-type matrix equations, efficiently solvable using available software like MATLAB. To validate the accuracy of our proposed numerical method, we compare it with exact solutions and achieve promising results in comparison with other numerical solvers introduced in existing literature.
Czech name
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Czech description
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Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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