Huitzilín Yépez-Martínez - Universidad Autónoma de la Ciudad de México, Prolongación San Isidro ۱۵۱, Col. San Lorenzo Tezonco, Del. Iztapalapa, C.P. ۰۹۷۹۰ México D.F., México
José Francisco Gómez-Aguilar - Departamento de Ingeniería Electrónica, CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. ۶۲۴۹۰, Cuernavaca Morelos, México

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.

Variational iteration method, Fractional calculus, Laplace transform, Modified Caputo-Fabrizio fractional derivative, Modified Atangana-Baleanu fractional derivative