Resumen de Contributions to conformable and non-conformable calculus

Alberto Fleitas Imbert

• In this work, we introduce a definition of a local fractional derivative and a fractional integral of order alpha >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 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, applications of the fractional derivative through the direct and inverse problems are shown, as well as the feasibility of the fractional calculus in real and simulated problems.