Detailed Error Analysis for a Fractional Adams Method on Caputo–Hadamard Fractional Differential Equations

Abstract

We consider a predictor–corrector numerical method for solving Caputo–Hadamard fractional differential equation over the uniform mesh logtj=loga+logtNajN,j=0,1,2,…,N with a≥1, where loga=logt0logt1…logtN=logT is a partition of [loga,logT]. The error estimates under the different smoothness properties of the solution y and the nonlinear function f are studied. Numerical examples are given to verify that the numerical results are consistent with the theoretical results.

Keywords

• predictor–corrector method
• Caputo–Hadamard fractional derivative
• uniform meshes
• error estimates
• Adams–Bashforth–Moulton method
• smoothness properties