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Fractional Calculus(FC)started in 1695 when LH(o)pital wrote a letter to Leibniz asking for the meaning of Dny for n = 1/2.Starting with the ideas of Leibniz many important mathematicians developed the theoretical concepts,but the area remained untouched in physics and engineering.During the last two decades FC emerged associated with phenomena with long range memory such as chaos and,consequently,in the modeling of dynamical systems.This lecture introduces the FC fundamental mathematical concepts,presents several applications and discusses future challenges.