Green’s Function for the Fractional KDV Equation on the Periodic Domain via Mittag-Leffler Function

The linear operator c + (??)?/2, where > 0 and (??)?/2 is the fractional Laplacian on periodic domain, arises in existence of travelling waves Korteweg-de Vries equation. We establish a relation Green function this with Mittag-Leffler function, which was previously used context Riemann-Liouville Caputo derivatives. By using relation, we prove that strictly positive single-lobe (monotonically decreasing away from maximum point) for every ? ? (0, 2]. On other hand, argue numerical approximations case (2, 4], small non-positive non-single lobe large c.