A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10256733" target="_blank" >RIV/61989100:27740/24:10256733 - isvavai.cz</a>

Výsledek na webu

<a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0313860" target="_blank" >https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0313860</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1371/journal.pone.0313860" target="_blank" >10.1371/journal.pone.0313860</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives

Popis výsledku v původním jazyce

Fractional nonlinear partial differential equations are used in many scientific fields to model various processes, although most of these equations lack closed-form solutions. For this reason, methods for approximating solutions that occasionally yield closed-form solutions are crucial for solving these equations. This study introduces a novel technique that combines the residual function and a modified fractional power series with the Elzaki transform to solve various nonlinear problems within the Caputo derivative framework. The accuracy and effectiveness of our approach are validated through analyses of absolute, relative, and residual errors. We utilize the limit principle at zero to identify the coefficients of the series solution terms, while other methods, including variational iteration, homotopy perturbation, and Adomian, depend on integration. In contrast, the residual power series method uses differentiation, and both approaches encounter difficulties in fractional contexts. Furthermore, the effectiveness of our approach in addressing nonlinear problems without relying on Adomian and He polynomials enhances its superiority over various approximate series solution techniques.

Název v anglickém jazyce

A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives

Popis výsledku anglicky

Fractional nonlinear partial differential equations are used in many scientific fields to model various processes, although most of these equations lack closed-form solutions. For this reason, methods for approximating solutions that occasionally yield closed-form solutions are crucial for solving these equations. This study introduces a novel technique that combines the residual function and a modified fractional power series with the Elzaki transform to solve various nonlinear problems within the Caputo derivative framework. The accuracy and effectiveness of our approach are validated through analyses of absolute, relative, and residual errors. We utilize the limit principle at zero to identify the coefficients of the series solution terms, while other methods, including variational iteration, homotopy perturbation, and Adomian, depend on integration. In contrast, the residual power series method uses differentiation, and both approaches encounter difficulties in fractional contexts. Furthermore, the effectiveness of our approach in addressing nonlinear problems without relying on Adomian and He polynomials enhances its superiority over various approximate series solution techniques.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

—

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

PLoS One

ISSN

1932-6203

e-ISSN

1932-6203

Svazek periodika

19

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

—

Kód UT WoS článku

001397531300039

EID výsledku v databázi Scopus

2-s2.0-85213374604