Numerical Methods for Solving a Riesz Space Partial Fractional Differential Equation: Applied to Fractional Kinetic Equations

In this paper, we design new numerical methods for solving the partial fractional differential equations. The fractional kinetics equation has been considered in this paper. The Riesz fractional derivative has been approximated by linear interpolation polynomial and numerical methods have been designed by using the Euler and the Crank–Nicolson methods. Furthermore, the error bounds of proposed methods are obtained. We also show that our numerical methods are stable and convergent with the accuracy of O ( κ + h ) and O ( κ 2 + h ) respectively. Finally, some numerical examples are constructed to demonstrate the efficacy and usefulness of the numerical methods.