In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these thinks in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman–Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald–Letnikov approach, which is power series expansion of the generating function. Having the thinking in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman-Feshbach Tikochinsky oscillator. numerical analysis of the corresponding fractional Euler-Lagrange equations is within within the Grünwald-Letnikov approach, which is power series expansion of the generating function.