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 kernel is presented; in particular, the caputo-fabrizio fractional derivative and the atangana-baleanu fractional derivative with the non-singular kernel is considered. the analysis elaborated for both non-singular kernel 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 kernel in order to satisfy the initial conditions for some fractional differential equations