An efficient method for the analytical study of linear and nonlinear time-fractional partial differential equations with variable coefficients

Basit Öğe Kaydı
dc.authoridProsviryakov, Evgenii/0000-0002-2349-7801
dc.contributor.authorLiaqat, M. I.
dc.contributor.authorAkgul, A.
dc.contributor.authorProsviryakov, E. Yu.
dc.date.accessioned2024-12-24T19:30:01Z
dc.date.available2024-12-24T19:30:01Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractThe residual power series method is effective for obtaining approximate analytical solutions to fractional-order differential equations. This method, however, requires the derivative to compute the coefficients of terms in a series solution. Other well-known methods, such as the homotopy perturbation, the Adomian decomposition, and the variational iteration methods, need integration. We are all aware of how difficult it is to calculate the fractional derivative and integration of a function. As a result, the use of the methods mentioned above is somewhat constrained. In this research work, approximate and exact analytical solutions to time-fractional partial differential equations with variable coefficients are obtained using the Laplace residual power series method in the sense of the Gerasimov-Caputo fractional derivative. This method helped us overcome the limitations of the various methods. The Laplace residual power series method performs exceptionally well in computing the coefficients of terms in a series solution by applying the straightforward limit principle at infinity, and it is also more effective than various series solution methods due to the avoidance of Adomian and He polynomials to solve nonlinear problems. The relative, recurrence, and absolute errors of the three problems are investigated in order to evaluate the validity of our method. The results show that the proposed method can be a suitable alternative to the various series solution methods when solving time-fractional partial differential equations.
dc.identifier.doi10.14498/vsgtu2009
dc.identifier.endpage240
dc.identifier.issn1991-8615
dc.identifier.issn2310-7081
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85174953852
dc.identifier.scopusqualityQ3
dc.identifier.startpage214
dc.identifier.urihttps://doi.org/10.14498/vsgtu2009
dc.identifier.urihttps://hdl.handle.net/20.500.12604/7340
dc.identifier.volume27
dc.identifier.wosWOS:001100245300002
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSamara State Technical Univ
dc.relation.ispartofVestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta-Seriya-Fiziko-Matematicheskiye Nauki
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectLaplace transform
dc.subjectresidual power series method
dc.subjectpartial diffe-rential equation
dc.subjectGerasimov-Caputo derivative
dc.titleAn efficient method for the analytical study of linear and nonlinear time-fractional partial differential equations with variable coefficients
dc.typeArticle

Dosyalar

Koleksiyon

WOS İndeksli Yayınlar Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu