A novel diffusive representation of fractional calculus to stability and stabilisation of noncommensurate fractional-order nonlinear systems

The article shows a new tantamount description of Caputo's fractional calculus through use of an assistant binary function. Applying the concepts of Laguerre's function and its integration, an original approximative method of the consequent infinitely dimensional state space model is proposed. And it is indispensable to exhibit the validity and superiority of our given scheme by contrast to some relevant researching findings of the theoretical results before. Meantime, some questions of diffusive representation for fractional calculus in existing references are pointed out. The proposed diffusive representation in this article can be also provided to analyze and control a kind of noncommensurate fractional order non-autonomous systems. Finally, two examples associated with numerical simulations are used to support our obtained approximation method and stability criterions.