Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients

Abstract

Abstract:The time and space fractional wave and heat type equations with variable coefficients are considered, and the variable order derivative in He's fractional derivative sense are taken. The utility of the homotopy analysis fractional sumudu transform method is shown in the form of a series solution for these generalized fractional order equations. Some discussion with examples are presented to explain the accuracy and ease of the method.

A fractional model and its application to heat prevention coating with cocoon-like hierarchy

“…There are many definitions of fractional derivatives, this paper adopts the variational iteration algorithm-based definition, and it is called as He's fractional derivative [22] or the fractional derivative in Ji Huan He's sense [23] in the literature. The VIM was first used to solve fractional differential equations in [24], and it has been proved to be effective, easy, and accurate to solve a lot of non-linear differential problems with the approximate values converging rapidly to the exact solutions.…”