Fractional Differential Transform Method

Abstract

Differential transform method (DTM) was initially proposed by Zhou (1986) to solve linear and nonlinear initial value problems with respect to the electrical circuit. DTM is a semi-analytical method based on the Taylor series expansion. The basic concept of DTM and some related theorems are first discussed in this chapter. Further, this method is used to address two problems, viz. linear fractional one-dimensional heat-like equation and nonlinear fractional advection equation. The test problems used in this chapter show that the DTM is another effective method for solving linear/nonlinear fractional differential equations. Usually, the series converges with an increase in terms, but again the compact form of the solution may not always be expected.