The coupled J-M equations are arising in different fields of science and engineering such as fluid mechanics, condense matter physics, optics, and plasma physics. In this study, a numerical approach is introduced for investigating the numerical solutions of the fractional order of coupled coupled J-M system. For this purpose, the fractional Bernoulli wavelets via spectral collocation method are employed to reducing the system of fractional order differential equations to some nonlinear system of algebraic equations. Finally, we utilize Newton iterative approach for solving the achieved nonlinear system. For showing the accuracy and efficiency of the purposed method, the solutions of some cases of coupled J-M system are provided.
