A fourth-order compact difference method for the nonlinear time-fractional fourth-order reaction–diffusion equation

A nonuniform linearized Galerkin‐spectral method for nonlinear fractional pseudo‐parabolic equations based on admissible regularities

“…Recently, several numerical schemes have been proposed for the solution of FPPEs in which the assumption of smoothness of the solution in time is considered. [12][13][14][15] It should be noted that this assumption is unrealistic because fractional problems have a singularity at the beginning of time. The solution to (1.1) is non-smooth in the time direction.…”

Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations

“…Meanwhile, various numerical and analytical methods have been proposed to solve problems involving these derivatives. For instance, see [10] , [11] , [12] , [13] . By integrating fractional derivatives with respect to the order of the derivative in a given interval, another family of fractional derivatives called the distributed-order fractional derivatives is produced [14] , [15] .…”

Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations

“…O h τ + by using the compact technique. Haghi et al [7] proposed a high-order compact numerical scheme for solving the two-dimensional nonlinear time-fractional fourthorder reaction-diffusion equation, the unique solvability of the numerical method is proved in detail. In addition, Li and Deng [13] proposed tempered weighted and shifted Grünwald difference operators for the Riemann-Liouville tempered fractional derivatives, and then a class of second-order numerical schemes is proposed for solving two-sided space tempered fractional diffusion equation.…”