Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 15Citation - Scopus: 18New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices(Asme, 2019) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; Yousef, FerasHerein, 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.Article Citation - WoS: 25Citation - Scopus: 32Ternary-Fractional Differential Transform Schema: Theory and Application(Springer, 2019) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; Yousef, FerasIn this article, we propose a novel fractional generalization of the three-dimensional differential transform method, namely the ternary-fractional differential transform method, that extends its applicability to encompass initial value problems in the fractal 3D space. Several illustrative applications, including the Schrodinger, wave, Klein-Gordon, telegraph, and Burgers' models that are fully embedded in the fractal 3D space, are considered to demonstrate the superiority of the proposed method compared with other generalized methods in the literature. The obtained solution is expressed in a form of an (alpha) over bar -fractional power series, with easily computed coefficients, that converges rapidly to its closed-form solution. Moreover, the projection of the solutions into the integer 3D space corresponds with the solutions of the classical copies for these models. This reveals that the suggested technique is effective and accurate for handling many other linear and nonlinear models in the fractal 3D space. Thus, research on this trend is worth tracking.