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AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE

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2019

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Abstract

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.

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Memory Index (Fractional Derivative), Fractional Partial Differential Equations, Solutions in Closed Form

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Alquran, Marwan...et al. (2019). "AN ANALYTICAL STUDY OF (2+1)-DIMENSIONAL PHYSICAL MODELS EMBEDDED ENTIRELY IN FRACTAL SPACE", Romanian Journal of Physics, Vol. 64, No. 1-2.

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Romanian Journal of Physics

Volume

64

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1-2

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