A new fractional derivative operator and applications

We introduce a new fractional derivative which obeys classical properties including linearity, product rule, power rule, vanishing derivatives for constant functions, chain rule, quotient rule, Rolle's Theorem and the Mean Value Theorem:D^\alpha(f)(t)=\lim _{\epsilon \rightarrow ۰} \frac{f\left(t e^{\frac{۱}{\Gamma(۱-\alpha)}} e^{-\alpha}\right)-f(t)}{\epsilon},this definition is comfortable with the classical definition of the Caputo Fractional Operator.

Keywords:

New Fractional Derivative , Fractional differential equations , Caputo differential operators