Finite difference methods for nonlinear fractional differential equation with [formula omitted]-Caputo derivative

Abstract

In this article, we construct finite difference methods for nonlinear fractional differential equation with ψ-Caputo derivative. The rectangle, Lψ,1 interpolation, and predictor–corrector methods on non-uniform meshes are proposed. The numerical stability analysis and error estimates are displayed. Numerical examples are also given to illustrate the theoretical results, where the chaotic attractors in the Lorenz system are numerically simulated in the sense of positivity of the largest Lyapunov exponent.