New Generalized Definition of Conformable Fractional Derivative

Abstract

In this paper we find new generalized definition of conformable fractional derivative. The definition satisfies linearity property, product rule for derivative, quotient rule for derivative and derivative of constant is zero. compare the chain rule formula of ordinary derivative and chain rule satisfied by new generalized definition of conformable fractional derivative. chain rule for like first order derivative are not satisfied. This can be proved by giving example and find derivatives of some standard functions by new generalized definition of fractional derivative. We introduced new generalized definition of conformable fractional derivative. We conclude that this definition coinside with the classical definition of derivative alpha=1. We introduce definition For alpha belongs to (0,1] and generalize for any alpha belongs to (n,n+1]