Numerical simulation of telegraph and Cattaneo fractional-type models using adaptive reproducing kernel framework

In this article, a class of generalized telegraph and Cattaneo time-fractional models along with Robin's initial-boundary conditions is considered using the adaptive reproducing kernel framework. Accordingly, a relatively novel numerical treatment is introduced to investigate and interpret approximate solutions to telegraph and Cattaneo models of time-fractional derivatives in Caputo sense. This treatment optimized solutions relying on the Sobolev spaces and Schmidt orthogonalization process that can be directly implemented to generate Fourier expansion at a rapid convergence rate, in which the arbitrary kernel functions satisfy Robin's homogeneous conditions. Furthermore, the solution is displayed in a fractional series formula in complete Hilbert spaces without any restrictive hypothesis on the desired issues. The effectiveness, validity, and potentiality of the proposed procedure are demonstrated by testing some applications. The graphical consequences indicate that the method is superior, accurate, and convenient in solving such fractional models.