Some Aspects of Numerical Analysis for a Model Nonlinear Fractional Variable Order Equation

The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of nonlinear, ordinary differential equation with derivative fractional variable order Gerasimov–Caputo type. questions approximation, convergence, and stability this are studied. It is shown that conditionally stable converges to first order. Using Riccati as an example, computational accuracy method analyzed. increase in nodes grid, tends unity, i.e., theoretical value accuracy.