A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives.
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Dosyalar
Tarih
2024
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Public Library of Science
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Algorithms, Models, Theoretical, Nonlinear Dynamics
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Khan, Z. A., Riaz, M. B., Liaqat, M. I., & Akgül, A. (2024). A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives. PloS one, 19(12), e0313860.
