A modification of the reduced differential transform method for fractional calculus

Abstract

In this paper, the reduced differential transform method is modified and successfully used to solve the fractional heat transfer equations. The numerical examples show that the new method is efficient, simple, and accurate.

Two-scale mathematics and fractional calculus for thermodynamics

“…Fractional calculus and fractal calculus are good candidates for discontinuous problems [2][3][4][5][6][7][8][9]. In continuum mechanics, we have the following Green formulae to build up governing equations:…”

An improved homotopy perturbation method for solving local fractional nonlinear oscillators

“…There are many computational methods for handling these fractional differential equations, such as the reduced differential transform method, 22 the transform methods, 23 the Yang Laplace transform-DJ iteration method, 24 the local fractional Fourier method, 25,26 and others. [15][16][17] Fractional oscillation equations arise in various areas of engineering and applied sciences, which are used as a powerful tool to vibration isolation and reduction of unnecessary vibration by porous media.…”

A new approximate analytical method for a system of fractional differential equations

“…where the fractional derivative is understood in the Caputo sense [14], α and β are parameters describing the order of the Caputo fractional derivative (0 < α ≤ 1, 0 < β ≤ 1), and f, g, φ, and ψ are given functions. Such systems arise in various areas, especially in the study of chemical reactions, in population dynamics and in mathematical biology [15][16][17][18][19][20][21].…”