The Invariant Subspace Method for Solving Fractional Partial Differential Equations

The Invariant Subspace Method for Solving Fractional Partial Differential Equations

Mohamed Soror Abdel Latif (Mansoura University, Egypt) and Abass Hassan Abdel Kader (Mansoura University, Egypt)
DOI: 10.4018/978-1-7998-3122-8.ch012

Abstract

In this chapter, the authors discuss the effectiveness of the invariant subspace method (ISM) for solving fractional partial differential equations. For this purpose, they have chosen a nonlinear time fractional partial differential equation (PDE) with variable coefficients to be investigated through this method. One-, two-, and three-dimensional invariant subspace classifications have been performed for this equation. Some new exact solutions have been obtained using the ISM. Also, the authors give a comparison between this method and the homogeneous balance principle (HBP).
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Invariant Subspace Method (Sahadevan & Parakash, 2017)

The ISM can be used for solving the following fractional PDE with order n

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