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

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

10103 - Statistics and probability

Projekt

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Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

The Fundamentals of Fractional Calculus

ISBN

978-1-00-363833-9

Počet stran výsledku

26

Strana od-do

324-349

Počet stran knihy

522

Název nakladatele

Apple Academic Press

Místo vydání

New York

Kód UT WoS kapitoly

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