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Solution for time-fractional coupled Klein-Gordon Schrödinger equation using decomposition method. (English) Zbl 1250.65125
Summary: The time-fractional coupled Klein-Gordon Schrödinger equation is obtained from the coupled Klein-Gordon Schrödinger equation by replacing the order time derivative with a fractional derivative of order $\alpha \in$(1,2], $\beta \in$(0,1]. The fractional derivative is described in the Caputo sense. In this study, a system of time-fractional coupled Klein-Gordon Schrödinger equations is considered with initial values and the solutions are presented using the Adomian decomposition method. The solutions of the equation are presented and the figures show the effectiveness and good accuracy of the proposed method.

##### MSC:
 65M99 Numerical methods for IVP of PDE 35Q40 PDEs in connection with quantum mechanics 35Q55 NLS-like (nonlinear Schrödinger) equations 35R11 Fractional partial differential equations
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