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This paper is concerned with the construction of biorthogonal multiwavelet basis in the unit interval to form a biorthogonal flatlet multiwavelet system. Next a method to calculate integer and fractional derivatives of the dual flatlet multiwavelets by multiplying some matrices is suggested. The system is then used to solve a fractional convection–diffusion equation. The biorthogonality and high vanishing moments properties of this system result in efficient and accurate solutions. Finally, numerical results for some test problems with known solutions are presented and the absolute errors are compared with the errors resulting from the other bases.

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In this paper, the modification of He's variational iteration method (MVIM) is developed to solve fractional integrodifferential equations with nonlocal boundary conditions. It is shown that by choosing suitable initial approximation, the exact solution obtains by one iteration. It is illustrated that the propose method is effective and has high convergency rate.