A New Conformable Fractional Derivative and Applications

Abstract

This paper is motivated by some papers treating the fractional derivatives. We introduce a new definition of fractional derivative which obeys classical properties including linearity, product rule, quotient rule, power rule, chain rule, Rolle’s theorem, and the mean value theorem. The definition Dαft=limh⟶0ft+heα−1t−ft/h, for all t>0, and α∈0,1. If α=0, this definition coincides to the classical definition of the first order of the function f.