Solution of fractional Klein-Gordon-Schrödinger equation with q-HAM method

Fractional analysis, which has a wide range of applications in science and engineering, is an important mathematical analysis branch in which derivatives and integrals are extended to non-integer orders. Our aim is to find a solution for the fractional Klein-Gordon-Schrödinger equation with the help of q-homotopy (q-HAM) analysis transformation method by using Atangana-Baleanu derivative. The solution method used is a combination of q-HAM and Laplace transform. In this study, firstly, the definitions and theorems required for the mentioned model are given. Then, the homotopy analysis method is explained., with this method, a solution for the fractional Klein-Gordon-Schrödinger (FKGS) equation is obtained. In order to better understand the relationship between the solutions obtained, various graphs with different parameter values are presented and comparison is made with the classical derivative. The results obtained reveal the advantages of arbitrary order of derivatives.