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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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