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

Physical processes with memory and hereditary properties can be best described by fractional differential equations due to 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 differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic B-spline functions are presented. The main characteristic of the approach is that it converts such problems into a system of algebraic equations which is suitable for computer programming. It not only simplifies the problem but also speeds up the computation. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation.

► In the present paper the fractional differential equations are investigated.
► Cubic B-spline wavelet collocation method is presented to find its solution.
► The method is based on analytical expressions of fractional derivatives in Caputo sense for cubic spline functions.
► The main problem is converted into those of solving a system of algebraic equations.
► The method is demonstrated on several examples to show its validity.