Spectral solution of fractional fourth order partial integro-differential equations

In this paper, mixed spectral method is applied to solve the fractional fourth order partial integro-differential equations together with weak singularity. Eigen-functions of the fourth order self-adjoint positive-definite differential operator are used for the discretization of spatial variable and its derivatives. Also, shifted Legendre polynomials are applied to the discretization of time variable. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach. The method is easy to apply and produces very accurate numerical results.