On the Solution of Fractional Order KdV Equation and Its Periodicity on Bounded Domain Using Radial Basis Functions

Abstract

The Coimbra concept of fractional order derivative is used to build a numerical approach using radial functions in this paper. The Coimbra derivative is capable of modelling a dynamic system with varying fractional order behaviour over time. The proposed scheme’s stability and convergence are investigated. In one and two space dimensions, the developed approach is validated for the given model. By applying a periodic boundary condition on a bounded domain, the model’s periodicity is shown statistically. The acquired findings demonstrate the new numerical scheme’s potency and, as a result, its high order accuracy.