On The k-Caputo-Fabrizio Fractional Derivative and its Applications

Abstract

In this paper a generalization of the derivative due to Caputo and Fabrizio in [3] is introduced. We present some useful properties, evaluate its Laplace transform and also obtain the k-fractional integral associated with the new fractional derivative. We will also resolving the k-fractional logistic equation Given by Cerutti [4] with a new fractional operator called on the k-Caputo-Fabrizios fractional derivative with a non-singular kernel. In the same way we will see that when $k=a=1$ the solution matches with the one given by Camargo and Bruno-Alfonzo [6].