Comparing Two Wavelet Approaches for Solving Fractional Differential Equations

Fractional calculus can be considered as rapidly developing research area widening limits of traditional computing. Current study is focused on development of numerical methods for solving fractional order differential equations using Haar wavelet methods. There are two Haar wavelet based approaches available in literature for solving fractional order differential equations. These two approaches are analyzed. Furthermore, the refined wavelet expansion is proposed in the case where the order of fractional derivative is less than one. The theoretical approach introduced is validated by numerical analysis.