COMPUTATIONAL ADVANCEMENTS IN SPECTRAL METHODS FOR SOLVING FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258134" target="_blank" >RIV/61989100:27740/25:10258134 - isvavai.cz</a>

Result on the web

<a href="https://www.worldscientific.com/doi/epdf/10.1142/S0218348X25401218" target="_blank" >https://www.worldscientific.com/doi/epdf/10.1142/S0218348X25401218</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218348X25401218" target="_blank" >10.1142/S0218348X25401218</a>

Result language

angličtina

Original language name

COMPUTATIONAL ADVANCEMENTS IN SPECTRAL METHODS FOR SOLVING FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS

Original language description

In this paper, we broaden the applicability of the operational matrices associated with Vieta-Lucas polynomials by introducing a modified, computationally efficient method. This method is designed within the spectrum of spectral methods to address Bagley-Torvik types of fractional derivative differential equations (FDDE). The Bagley-Torvik equation involves both integer-order and fractional-order derivatives, along with diverse source terms and non-homogeneous initial conditions, making it challenging to find exact solutions. In response to these complexities, we propose a modified spectral method capable of handling Bagley-Torvik types of FDDE with both homogeneous and non-homogeneous initial conditions as well as diverse source terms. The source terms are approximated using a basis set comprising Vieta-Lucas polynomials, while the fractional-order derivative terms in the problems are approximated using the newly proposed fractional-order integral operational matrix. Through the implementation of these approximations, the FDDE is transformed into a system of matrix equations, without the need for implementing the spectral Tau method. The results derived from this proposed technique are compared with other methods, including existing exact solutions. This comparison shows that the results are computed accurately and within a significantly shorter duration by our proposed method. Additionally, we broaden the domain of the proposed technique by solving more generalized FDDE with initial conditions.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

21100 - Other engineering and technologies

Project

—

Continuities

O - Projekt operacniho programu

Publication year

2025

Confidentiality

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

Name of the periodical

Fractals

ISSN

0218-348X

e-ISSN

1793-6543

Volume of the periodical

33

Issue of the periodical within the volume

06

Country of publishing house

SG - SINGAPORE

Number of pages

17

Pages from-to

'2540121-1'-'2540121-17'

UT code for WoS article

001519242800001

EID of the result in the Scopus database

2-s2.0-105009431333