Abstract
The manuscript studies the four dimensional fractional order biological snap oscillator. Its thorough dynamical analysis is performed using dynamical tools such as phase portraits, Lyapunov and bifurcation analysis, system’s solution, stagnation points analysis etc. The impact of fractional order on the chaotic system is also discussed by plotting phase diagrams, Lyapunov and bifurcation diagrams for variable order. Considering uncertainties and disturbances trajectories are stabilized about its unique stagnation point using adaptive SMC technique. The controllers are constructed to compensate undesirable chaotic/ hyper chaotic behavior of the biological system which may give rise to fatal health pathological conditions. Also SMC technique show immediate effect in controlling of chaos in the system. Numerical simulations are performed using MATLAB.