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In this paper, a novel formula expressing explicitly the fractional-orderderivatives, in the sense of Riesz-Feller operator, of Jacobi polynomials ispresented. Jacobi spectral collocation method together with trapezoidal ruleare used to reduce the fractional L\'{e}vy-Feller advection-dispersion equation(LFADE) to a system of algebraic equations which greatly simplifies solvinglike this fractional differential equation. Numerical simulations with somecomparisons are introduced to confirm the effectiveness and reliability of theproposed technique for the L\'{e}vy-Feller fractional partial differentialequations.

Efficient method for fractional L\'{e}vy-Feller advection-dispersion equation using Jacobi polynomials