DSpace Repository

Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations

Show simple item record

dc.contributor.author Heydari, Mohammad Hossein
dc.contributor.author Razzaghi, Mohsen
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2024-05-02T11:52:59Z
dc.date.available 2024-05-02T11:52:59Z
dc.date.issued 2023-07
dc.identifier.citation Heydari, Mohammad Hossein; Razzaghi, Mohsen; Baleanu, Dumitru. (2023). "Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations", Journal of Advanced Research, Vol.49, pp.175-190. tr_TR
dc.identifier.issn 20901232
dc.identifier.uri http://hdl.handle.net/20.500.12416/8125
dc.description.abstract Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement of the consideration problem alone. In defining this kind of derivatives, several types of fractional derivatives can be used simultaneously. Objectives: This study introduces a new kind of piecewise fractional derivative by employing the Caputo type distributed-order fractional derivative and ABC fractional derivative. The one- and two-dimensional piecewise fractional Galilei invariant advection–diffusion equations are defined using this piecewise fractional derivative. Methods: A new class of basis functions called the orthonormal piecewise Vieta-Lucas (VL) functions are defined. Fractional derivatives of these functions in the Caputo and ABC senses are computed. These functions are utilized to construct two numerical methods for solving the introduced problems under non-local boundary conditions. The proposed methods convert solving the original problems into solving systems of algebraic equations. Results: The accuracy and convergence order of the proposed methods are examined by solving several examples. The obtained results are investigated, numerically. Conclusion: This study introduces a kind of piecewise fractional derivative. This derivative is employed to define the one- and two-dimensional piecewise fractional Galilei invariant advection–diffusion equations. Two numerical methods based on the orthonormal VL polynomials and orthonormal piecewise VL functions are established for these problems. The numerical results ob tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1016/j.jare.2022.10.002 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Galilei Invariant Advection–Diffusion Equations tr_TR
dc.subject Orthonormal Piecewise Vieta-Lucas Functions tr_TR
dc.subject Orthonormal Vieta-Lucas Polynomials tr_TR
dc.subject Piecewise Fractional Derivative tr_TR
dc.title Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations tr_TR
dc.type article tr_TR
dc.relation.journal Journal of Advanced Research tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 49 tr_TR
dc.identifier.startpage 175 tr_TR
dc.identifier.endpage 190 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


Files in this item

This item appears in the following Collection(s)

Show simple item record