A novel Fourier-based meshless method for [formula omitted]-dimensional fractional partial differential equation with general time-dependent boundary conditions

Abstract

The article presents the novel Fourier-based meshless technique for solving (3+1)-dimensional fractional partial differential equation with coefficients varying in time under time-dependent boundary conditions of the general form. We transform the original equation into the one with homogeneous boundary conditions using a smooth analytical function and apply the Fourier expansion over the system of eigenfunctions of the Laplace operator corresponding to the zero boundary conditions which are solved independently using the semi-analytical backward substitution technique with the Müntz polynomial basis. The proposed method also can be used to solve problems of the integer orders or stationary ones where the Fourier expansion technique is suitable. The accuracy and efficiency of the mentioned procedure are demonstrated by solving high orders fractional equations.