Go through literature. Most of the numerical work in fPDE is by Haar, Chebychev, Legendre wavelets and by Bernstein polynomials.
Thank you dear Mittal, It is necessary for me that theoretical infrastructures of the methods.
I suggest that you read this nice paper http://www.hindawi.com/journals/aaa/2013/562140/
Dear Toufic El Arwadi, the article that suggested to me is very nice, thank you very much.
We have recently published some work on the use of Fourier methods for fractional reaction-diffusion equations written in terms of the fractional Laplacian. These methods are highly efficient and accurate, and extremely easy to implement (codes provided in the main text).
Article Fourier spectral methods for fractional-in-space reaction-di...
Dear scientists, thank you very much for your helpful answers,
There are a lot of efficient and accurate methods about the PDEs fractional order, but can someone use these methods in option pricing (Black-Scholes or etc.) because of arbitrage?
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