Abstract
This paper uses the differential transform method (DTM) to obtain analytical solutions of fractional heat- and wave-like equations with variable coefficients. The time fractional heat-like and wave-like equations with variable coefficients were obtained by replacing a first-order and a second-order time derivative by a fractional derivative of order . The approach mainly rests on the DTM which is one of the approximate methods. The method can easily be applied to many problems and is capable of reducing the size of computational work. Some examples are presented to show the efficiency and simplicity of the method.
Highlights
Fractional order partial differential equations, as generalizations of classical integer order partial differential equations, have been used to model problems in fluid flow and other areas of application
Fractional differentiation and integration operators were used for extensions of diffusion and wave equations [ ]
The main disadvantage of the Adomian method is that the solution procedure for calculation of Adomian polynomials is complex and difficult as pointed out by many researchers [ – ]
Summary
Fractional order partial differential equations, as generalizations of classical integer order partial differential equations, have been used to model problems in fluid flow and other areas of application. Momani [ ] applied the method to the time fractional heat-like and wave-like equations with variable coefficients. Xu and Cang [ ] solved the fractional heat-like and wave-like equations with variable coefficients using the homotopy analysis method (HAM). In , the variational iteration method (VIM) was first proposed to solve fractional differential equations with great success [ ].
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