High-Order Approximation to Generalized Caputo Derivatives and Generalized Fractional Advection–Diffusion Equations

In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate generalized Caputo fractional derivative (GCFD). Convergence order for (4−α), where α(0<α<1) of GCFD. The local truncation error also provided. Then, we adopt developed establish difference solution advection–diffusion equation with Dirichlet boundary conditions. Furthermore, discuss stability and convergence scheme. Numerical examples are presented examine theoretical claims. analyzed numerically, which (4−α) in time second-order space.