abstract 99

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

99

From conformable and no conformable fractional derivative to integer order calculus (Research Paper)

Rubén Gustavo Paccosi, Carlos Peña Rincón, Pablo Leandro Bonucci, Juan Eduardo Nápoles Valdéz.

In 2014 Khalil et al. introduced a new definition of a local fractional derivative called conformable fractional derivative (CFD). In 2019 Anderson et al. interpreted the Khalil's  derivative from integer order calculus as a simple change of variable. Simultaneously from 2014 others conformable derivatives have emerged.  All these derivatives depend on a particular kernel. In this article we study what properties the kernels can have in order for such conformable derivatives to be  interpreted from the integer order calculus making a change of variable. In other hand, in 2018 other local fractional derivative called non-conformable (NCFD) was presented. Regarding this last derivative, new theoretical studies have appeared that allow an even greater generalization of fractional derivates. We demonstrate that the NCFD can also be interpreted from the integer order calculus by making a change of variable. In summary, in this paper we give necessary conditions on the respective kernels so that both derivatives can be reinterpreted from integer-order calculus.

Keywords: Fractional derivative; non-conformable fractional derivative; conformable fractional derivative; fractional dynamical systems.

Cite this paper:

Paccosi R.G., Peña Rincón C., Bonucci P.L., Nápoles Valdéz J.E.

From conformable and no conformable fractional derivative to integer order calculus. 

Bull. Comput. Appl. Math. (Bull CompAMa), 

Vol. 12, No.2 pp.xx-xx, 2024.