The Schrödinger-KdV equation of fractional order with Mittag-Leffler nonsingular kernel
Mehmet Yavuz, Tukur Abdulkadir Sulaıman, Abdullahi Yusuf, Thabet Abdeljawad
Abstract
Fractional order differential equations are utilized for modeling many complicated physical and natural phenomena in nonlinear sciences and related fields. In this manuscript, the fractional order Schrödinger-KdV equation in the sense of Atangana-Baleanu derivative is investigated. The Schrödinger-KdV equation demonstrates various types of wave propagation such as Langmuir wave, dust-acoustic wave and electromagnetic waves in plasma physics. Using the fixed-point theorem, the existence and uniqueness to the solution of the studied nonlinear model is established. Using the modified Laplace decomposition method, we establish the exact solution to fractional order Schrödinger-KdV equation. The numerical simulations to the reported result are presented. The comparison between analytical and numerical approximations is also presented. It is shown that the approximate-analytical results are compatible with the analytical results via the L2 and L∞ error norms. We compare our result with some existing results in the literature.