Abstract
A numerical method for the modified time fractional Fokker-Planck equation is proposed. Stability and convergence of the method are rigorously discussed by means of the Fourier method. We prove that the difference scheme is unconditionally stable, and convergence order isO(τ+h4), whereτandhare the temporal and spatial step sizes, respectively. Finally, numerical results are given to confirm the theoretical analysis.
Highlights
Fractional differential equations have attracted considerable attention due to their frequent appearance in various applications in fluid mechanics, biology, physics, and engineering [1, 2]
We prove that the difference scheme is unconditionally stable, and convergence order is O(τ + h4), where τ and h are the temporal and spatial step sizes, respectively
The solvability, stability, and convergence of the numerical method are discussed in Sections 3 and 4, respectively
Summary
Fractional differential equations have attracted considerable attention due to their frequent appearance in various applications in fluid mechanics, biology, physics, and engineering [1, 2]. Fractional differential equations do not have analytic solutions and can only be solved by some semianalytical and numeric techniques. Several semianalytical methods, such as variational iteration method, homotopy perturbation method, Adomian decomposition method, homotopy analysis method, and collocation method, have been used to solve fractional differential equations [3,4,5,6,7]. We are motivated to study the following modified time fractional Fokker-Planck equation [18]:. The solvability, stability, and convergence of the numerical method are discussed in Sections 3 and 4, respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
