A meshless method to solve the variable-order fractional diffusion
problems with fourth-order derivative term
Using the meshless collocation method, a scheme for solving nonlinear
variable-order fractional diffusion equation with fourth-order
derivative term is presented. Here approximations to fractional
derivative term are obtained by weighted and shifted
Gr\”unwald difference (WSGD) approximation formula. The
difficulty caused by the nonlinear terms is carefully handled by
quasilinearization technique. Using the radial basis functions, the
solution of the problem is written in terms of the primary
approximation, and the related correcting functions at each time step.
Then the approximation is substituted back to the governing equations
where the unknown parameters can be determined. Finally, the method is
supported by several numerical experiment on irregular domains.