Some Fractional Derivatives with Different Kernels

Abstract

In this manuscript, we construct the constant proportional Caputo-Fabrizio and constant proportional Atanagana-Baleanu derivatives. We obtain the inverse operators of these derivatives by Laplace transform. We change the classical derivatives with proportional derivative in the Caputo-Fabrizio and Atangana-Baleanu derivatives. We can see the effect of the proportional derivative on these fractional derivatives. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.