A binary Caputo–Fabrizio fractional reproducing kernel method for the time-fractional Cattaneo equation

The fractional Cattaneo equation based on the Caputo–Fabrizio derivative is commonly utilized in physical science due to its hyperbolic property and nonsingular property. In this paper, we present a binary fractional reproducing kernel collocation method based on the Caputo–Fabrizio derivative for solving the time-fractional Cattaneo equation. The Caputo–Fabrizio fractional reproducing kernel space and its reproducing kernel function are proposed. On this basis, we construct a binary fractional reproducing kernel space as the solution space. A set of two-dimensional bases are constructed using the Caputo–Fabrizio fractional-order reproducing kernel function and the shifted Legendre reproducing kernel function, which in turn leads to the approximate solution of the problem. In addition, some detailed numerical analysis of the proposed algorithm, such as convergence and stability, is carried out. Numerical experiments verified the effectiveness and accuracy of our algorithm.