In this paper, a new approach for solving the system of fractional integro-differential equation with weakly singular kernels is introduced. The method based on class symmetric orthogonal polynomials called shifted sixth-kind Chebyshev polynomials. First, operational matrices are constructed, and after that, described. This reduces equations (WSFIDEs) by collocation into algebraic equations. Th...

—————————————————————————————————— – Abstract In this paper, we provide the collocation method for natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear waste disposal. This problem is a non-linear, three-point boundary value problem on semi-infinite interval. We use two orthogonal functions namely rational Gege...

A new method is formulated and analyzed for the approximate solution of a twodimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit (ADI) method based on the Crank-Nicolson method combined with the L1-approximation of the time Caputo derivative of...