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 $\left(D^{\alpha }f\right)\left(t\right)=\underset{h⟶0}{\text{lim}}\left(\left(f\left(t+h{e}^{\left(\alpha -1\right)t}\right)-f\left(t\right)\right)/h\right),$ for all $t>0$ , and $\alpha \in \left(\mathrm{0,1}\right)$ . If $\alpha =0$ , this definition coincides to the classical definition of the first order of the function $f$ .