Embedding (3+1)-dimensional diffusion, telegraph, and Burgers' equations into fractal 2D and 3D spaces: An analytical study

Fractional derivatives can be utilized as a promising tool for characterizing systems with embedded memory or describing viscoelasticity of advanced materials. Motivated by the significance of fractional derivatives, we provide assorted of analytical representations for the solution of higher-dimensional fractional differential equations that involve multi-memory indices. Then, an iterative parallel scheme of the power series method with underlying these representations is applied to extract fractal closed-form and supportive approximate solutions for several multi-memory models. Some of the obtained closed-form solutions are given in terms of the generalized exponential and hyperbolic functions which might be more suitable for representing nonlinear physical behaviors. (C) 2018 The Authors. Production and hosting by Elsevier B.V.