New Fractional Operators Theory and Applications

Document Type : Research Paper


Department of Mathematics, College of Science, AL-Mustansiriyah University, Baghdad, Iraq


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-19) transmission is presented as an application.