Abstract: Fractional Calculus has gained considerable development in the recent forty years, while in fact it is a subject of several hundred years as Calculus. Fractional integral and differential equations have been applied in many physical and engineering real-world problems, and have been verified as powerful tools in modeling particular phenomena with memory effect. In this talk, we will introduce the mathematical preliminaries of fractional calculus, including different definitions of fractional integrals and fractional derivatives, and some properties of fractional operators. Furthermore, we would like to introduce two types of generalized fractional operators, which contain all existing classical and fractional integrals and derivatives as special cases. Those generalized fractional operators are firstly proposed in 2010 and 2012, respectively. Nowadays it is opening some possible interests on fractional calculus. As an application, we finally discuss the dynamical behaviors of Harmonic oscillator and van der Pol oscillator with generalized fractional derivatives, which depends on different kernel functions. Many interesting dynamics may not appear in classical Harmonic and van der pol oscillators will be presented

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