Abstract: Fractional Calculus (FC) goes back to the inception of the theory of differential calculus. Nevertheless, theapplication of FC just developed in the recent two decades, due to the advancement in the domain of chaos that revealed subtlelinks with the FC notions. At the topic of dynamical systems theory, some work has been carried out but the proposed modelsand methods are still in a preliminary state of establishment. Having these notions in mind, the paper explores FC in the studyof system dynamics and control. In this context, this work analyses the usage of FC in the fields of controller tuning, leggedrobots, redundant robots, heat diffusion, and digital circuit synthesis. We explored review of fractional inequalities.Keywords: Fractional Calculus, Robot, Digital circuit synthesis, Engineering