The Spectral Methods of Investigation the Processes of Heterodiffusion in the Terms of Fractional Derivatives

In the work, a mathematical model of the heterodiffusion process using by fractional time derivatives are constructed. The boundary value problem is solved by the method of the separation of variables in the basis of orthogonal Jacobi polynomials is formulated. At the same time, the fractional time derivative is introduced through the Jacobi polynomials. A system of algebraic equations was built to find the unknown coefficients. For this the theorem which makes it possible to present the fractional derivatives in the form of Fourier-Jacobi series was proved. In this case, the solution of boundary value problems is reduced to the systems of differential equations in which there is no time derivative. The resulting system can be solved by both analytical and spectral methods. At the same time, in the case of using by the spectral method of finding a solution is reduced to finding unknown coefficients from a system of algebraic equations. The results were obtained in the study of heterodifusion processes in the layer.