%0 Journal Article
%T Laplace Variational Iteration Method for Modified Fractional Derivatives with Non-singular Kernel
%J Journal of Applied and Computational Mechanics
%I Shahid Chamran University of Ahvaz
%Z 2383-4536
%A Yépez-Martínez, Huitzilín
%A Gómez-Aguilar, José Francisco
%D 2020
%\ 07/01/2020
%V 6
%N 3
%P 684-698
%! Laplace Variational Iteration Method for Modified Fractional Derivatives with Non-singular Kernel
%K Variational iteration method
%K Fractional calculus
%K Laplace transform
%K Modified Caputo-Fabrizio fractional derivative
%K Modified Atangana-Baleanu fractional derivative
%R 10.22055/jacm.2019.31099.1827
%X 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.
%U https://jacm.scu.ac.ir/article_15045_be3144453e68d8e1ec1a2c082a8d54c8.pdf