Abstract
Fractional partial differential equations have many applications in science and engineering. However, not only the analytical solution existed for a limited number of cases, but also the numerical methods are very complicated and difficult. The aim of this paper is to present an efficient wavelet operational method based on the second Chebyshev wavelet to solve the fractional partial differential equations. We derived the convergence of the two-dimensional second Chebyshev wavelet and give the second Chebyshev wavelet operational matrix of fractional integration. Then we present a computational method based on the above results for solving a class of fractional partial differential equations. The initial equations are transformed into a Sylvester equation. Some numerical examples are given to demonstrate the simplicity, clarity and powerfulness of the new method.
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