The motivation for this paper comes from other papers treating the fractional derivatives. We introducea new definition of fractional derivative which obeys classical properties including linearity, product rule, quotient rule, power rule, chain rule, Rolle’s theorem, mean value theorem and Taylor series. Usage of thedefined derivative is given in the example section which shows how our derivative can be used in solving differential equations. Comparison of our derivative with the derivative defined by Abdejjawad and overall conclusions are given in the conclusion section.