New Fractional Operators Theory and Applications

In this article, we present a new fractional integral with a non-singular kernel and by using Laplace transform, we derived the corresponding fractional derivative. By composition between our fractional integration operator with classical Caputo and Riemann-Liouville fractional operators, we establish a new fractional derivative which is interpolated between the generalized fractional derivatives in a sense Riemann-Liouville and Caputo-Fabrizio with non-singular kernels. Additionally, we introduce the fundamental properties of these fractional operators with applications and simulations. Finally, a model of Coronavirus (COVID-۱۹) transmission is presented as an application.

Keywords:

Fractional integral , Fractional derivative , non-singular kernels , Mittag-Leffler function , Coronavirus (COVID-۱۹)