Many phenomena in viscoelasticity, fluid mechanics, biology, chemistry, acoustics, control theory, psychology, and other areas of science can be successfully modeled by the use of fractional order derivatives. That is because of the fact that, a realistic modeling of a physical phenomenon having dependence not only at the time instant, but also the previous time history can be successfully achieved by using fractional calculus. Some mechanical problems such as eigenvalue problem, higher-order initial problems, fractional integro-differential equations, etc., the governing equations are some complicated and cannot be solved by the traditional differential transformation method (DTM). This chapter introduces DTM for advance problems and contains the following sections:
2.1
Introduction
2.2
Differential Transformation Method for Higher-Order Initial Value Problems
2.3
Fractional Differential Transform Method
2.4
Differential Transformation Method for Integro-Differential Equation
2.5
Differential Transformation Method for Eigenvalue Problems
2.6
Two-Dimensional Differential Transformation Method for Fractional Order Partial Differential Equations
2.7
Reduced Differential Transform Method
2.8
Modified Differential Transformation Method
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