Note on the generalized conformable derivative

We introduce a definition of a generalized conformable derivative of order alfa > 0 (where this parameter does not need to be integer), with which we overcome some deficiencies of known local derivatives, conformable or not. This definition allows us to compute fractional derivatives of functions defined on any open set on the real line (and not just on the positive half- line). Moreover, we extend some classical results to the context of fractional derivatives. Also, we obtain results for the case alfa > 1The research of José M. Rodríguez and José M. Sigarreta is supported by a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00 / AEI /10.13039/501100011033), Spain