Laplace Variational Iteration Method for Modified Fractional Derivatives with Non-singular Kernel

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular keel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular keel is considered. The analysis elaborated for both non-singular keel derivatives is shown the necessity of considering the modified Caputo-Fabrizio fractional derivative and the analogous modifications for the Atangana-Baleanu fractional derivative with non-singular Mittag-Leffler keel in order to satisfy the initial conditions for some fractional differential equations.