Abstract. In this paper, a numerical method for solving a class of fractional partial differential equations with variable coefficients based on Chebyshev polynomials is proposed. The fractional derivative is described in the Caputo sense. The properties of Chebyshev polynomials are used to reduce the initial equations to the products of several matrixes. A system of linear equations are obtained by dispersing the coefficients and the products of matrixes. Only a small number of Chebyshev polynomials are needed to acquire a satisfactory result. Results obtained using the scheme presented here show that the numerical method is very effective and convenient for solving fractional partial differential equations with variable coefficients.

Abstract. In this paper, a generalization of differential electromagnetic equations in fractional space is provided. These equations can describe the behavior of electric and magnetic fields in any fractal media. The time evolution of the fractional electromagnetic waves by using the time fractional Maxwell's equations in fractional space has been investigated. Theoretical analysis shows that the amplitude variations of the general plane wave solution not only is related to Bessel functions, but also reveals an algebraic decay, at asymptotically large times.