Results on Katugampola Fractional Derivatives and Integrals

In this paper, we introduce and develop a new definitions for Katugampola derivative and Katugampola integral. In particular, we defined a (left) fractional derivative starting from a of a function f of order alpha is an element of (m - 1, m] and a (right) fractional derivative terminating at b, where m is an element of N. Then, we give some proprieties in relation to these operators such as linearity, product rule, quotient rule, power rule, chain rule, and vanishing derivatives for constant functions.