Progress in Fractional Differentiation & Applications

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This paper presents a practical formula expressing the fractional-order derivatives, in the sense of Riesz-Feller operator, of Jacobi polynomials. Jacobi spectral collocation method and the trapezoidal rule are used to reduce the fractional Le ́vy-Feller advection-dispersion equation (LFADE) to a system of algebraic equations which simplifies solving such fractional differential equation. Numerical simulations with some comparisons are introduced to confirm the effectiveness and reliability of the proposed technique for the Le ́vy-Feller fractional partial differential equations.

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