Abstract
This paper provides a numerical approach for solving the time-fractional Fokker–Planck equation (FFPE). The authors use the shifted Chebyshev collocation method and the finite difference method (FDM) to present the fractional Fokker–Planck equation into systems of nonlinear equations; the Newton–Raphson method is used to produce approximate results for the nonlinear systems. The results obtained from the FFPE demonstrate the simplicity and efficiency of the proposed method.
Highlights
Applications of fractional differential equation (FDE) in science and engineering are becoming vibrant, in the fields of physics, finance, viscoelasticity, chemistry, and fluid mechanics
Fractional differential equations (FDEs) cannot be solved using the exact methods [8,9,10], that is why the recent research has used the properties of shifted Chebyshev polynomials [14, 27] and the finite difference method (FDM) to simplify the fractional initial value problem (IVP) to a set of nonlinear equations
Using the properties of the shifted Chebyshev fourth-kind polynomials, we reduce the time-fractional Fokker–Planck equation to the system of differential equations
Summary
Applications of fractional differential equation (FDE) in science and engineering are becoming vibrant, in the fields of physics, finance, viscoelasticity, chemistry, and fluid mechanics. 3, the shifted Chebyshev collocation method and the finite difference method (FDM) are implemented to solve the fractional Fokker–Planck equation. The possible expression of the analytic form for the fourth-kind shifted Chebyshev polynomials Wn∗(t) of degree n is shown as follows: Wn∗(t) =
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