9 - Numerical method for a fractal–fractional ordinary differential equation with power law kernel

Abstract

In this chapter, ordinary differential equations with fractal–fractional derivatives with power law kernel are considered. These class of ordinary differential equations have been proven to capturing processes following at the same time power law and some self-similar behaviors. Due to their complexities, it is almost impossible to solve them using existing analytical methods. We make use of the two-steps Newton polynomial interpolation to derive a numerical scheme that will be used to solve these equations.