Numerical solution of fractional partial differential equations using cubic B-spline wavelet collocation method

Physical processes with memory and hereditary properties can be best described by fractional differential equations based on the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional partial differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic spline functions are presented. The main characteristic of the approach is that it converts such problems into those of solving a system of algebraic equations, which is suitable for numerical calculation. Numerical results demonstrate the validity and applicability of the method in solving fractional differential equation. The results from this method are good in terms of accuracy if the exact solution to fractional differential equation is in sufficient smooth.