A hybrid wavelet-meshless method for variable-order fractional regularized long-wave equation

This study employs a kind of non-singular variable-order fractional derivative to define a variable-order fractional version of the 2D regularized long-wave equation. The Legendre cardinal wavelets as a new family of the cardinal wavelets are introduced. A hybrid method based on the Legendre cardinal wavelets and radial basis functions is established to find the solution of this problem. This approach turns solving this equation into finding the solution of a nonlinear system of algebraic equations without utilizing discretization. The accuracy of the proposed technique is checked by solving four examples.