Numerical solution of fractional Fredholm integro-differential equations by spectral method with fractional basis functions

  title={Numerical solution of fractional Fredholm integro-differential equations by spectral method with fractional basis functions},
  author={Younes Talaei and Samad Noeiaghdam and Hossein Hosseinzadeh},
This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical polynomials such as Chebyshev, Legendre, Laguerre, etc, with a low order of convergence. For this reason, the development of classic numerical methods to solve such problems becomes a challenging issue. Since the non-smooth solutions have the same asymptotic… 

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