Computational Fractional Dynamical Systems

8Fractional Reduced Differential Transform Method

8.1 Introduction

In Chapter 7, we have discussed the differential transform method (DTM), which was first proposed by Zhou (1986), and it was used to solve linear and nonlinear initial value problems arising in electric circuit analysis. Later, DTM was used to solve partial differential equations. Another analytical version of DTM is the reduced differential transform method (RDTM). Recently, the RDTM has been found to be effective and reliable for handling linear and nonlinear partial differential equations and integral equations (Abazari and Kılıçman 2013; Abazari and Soltanalizadeh, 2013; Saravanan and Magesh 2013). Keskin and Oturanc (2010) applied this method to solve fractional differential equations with some modifications. Later this method was named as fractional reduced differential transform method (FRDTM). FRDTM has been successfully applied to solve various types of fractional partial differential equations (see Jena et al. (2019a, 2019b) and Saravanan and Magesh (2016)) and also higher‐dimensional problems (Rawashdeh 2015). In Chapters 3 and 5, we have implemented HPM and ADM, respectively, to solve some fractional‐order differential equations. The significant disadvantages of these approaches are that it requires complicated and plenty of calculations. In order to overcome such types of drawbacks, FRDTM has been introduced. The FRDTM is a computationally efficient and implementable analytical technique and provides ...