A high order predictor-corrector method with non-uniform meshes for fractional differential equations

This article proposes a predictor-corrector scheme for solving the fractional differential equations \({}_0^C D_t^\alpha y(t) = f(t,y(t)), \alpha >0\) ${}_0^C{D}_t^{\alpha }y(t)=f(t,y(t)),\alpha >0$ with non-uniform meshes. We reduce the fractional differential equation into the Volterra integral equation. Detailed error analysis and stability analysis are investigated. The convergent order of this method on non-uniform meshes is still 3 though \({}_0^C D_t^\alpha y(t)\) ${}_0^C{D}_t^{\alpha }y(t)$ is not smooth at \(t=0\) $t=0$ . Numerical examples are carried out to verify the theoretical analysis.