Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Alquran, MarwanSubject: search.filters.subject.Fractional Partial Differential Equations

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  • Article
    AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE
    (Editura ACAD Romane, 2019) Alquran, Marwan; Jaradat, Imad; Baleanu, Dumitru; Abdel-Muhsen, Ruwa
    In this article, we analytically furnish the solution of (2 + 1)-dimensional fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (alpha, beta, gamma)-fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor's theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting alpha, beta, gamma -> 1, which indicates to some extent for a sequential memory.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 18
    New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices
    (Asme, 2019) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; Yousef, Feras
    Herein, analytical solutions of three-dimensional (3D) diffusion, telegraph, and Burgers' models that are equipped with three memory indices are derived by using an innovative fractional generalization of the traditional differential transform method (DTM), namely, the threefold-fractional differential transform method (threefold-FDTM). This extends the applicability of DTM to comprise initial value problems in higher fractal spaces. The obtained solutions are expressed in the form of a (gamma) over bar -fractional power series which is a fractional adaptation of the classical Taylor series in several variables. Furthermore, the projection of these solutions into the integer space corresponds with the solutions of the classical copies for these models. The results detect that the suggested method is easy to implement, accurate, and very efficient in (non)linear fractional models. Thus, research on this trend is worth tracking.