Abstract

Herein, analytical solutions of 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 a form of a $\overline{\pmb{\gamma}}-$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 correspond 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 in this trend is worth tracking.

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