Abstract
The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.
Highlights
The history of fractional calculus is very long and the first idea appeared in Leibniz’s letter in 1695
We present an approximate analytical solution of the time fractional multi-dimensional diffusion equation of the order α(0 < α ≤ 1) in a series form which converges to exact solution rapidly, using fractional-order reduced differential transform method (FRDTM)
FRDTM is implemented successfully to find out the analytical solution of the time fractional-order multi-dimensional diffusion equation in terms of an infinite power series for the appropriate initial condition
Summary
The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multidimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations
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