An ε-Approximate Approach for Solving Variable-Order Fractional Differential Equations

As a mathematical tool, variable-order (VO) fractional calculus (FC) was developed rapidly in the engineering field due to it better describing anomalous diffusion problems engineering; thus, research of solutions VO differential equations (FDEs) has become hot topic for FC community. In this paper, we propose an effective numerical method, named as ε-approximate approach, based on least squares theory and idea residuals, VO-FDEs integro-differential (VO-FIDEs). First, VO-FIDEs are considered be analyzed appropriate Sobolev spaces H2n[0,1] corresponding orthonormal bases constructed scale functions. Then, space H2,02[0,1] is chosen which just suitable one models authors want solve demonstrate algorithm. Next, scheme given, stability convergence discussed. Finally, four examples with different characteristics shown, reflect accuracy, effectiveness, wide application