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 purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana-Baleanu fractional derivative. Since the new Atangana-Baleanu fractional derivative is non-singular and non-local, the Euler-Lagrange equations are proposed for the problems of Herglotz. Fractional variational Herglotz problems of variable order are considered and two cases are sho...

A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

The power law has been used to construct the derivative with fractional order in Caputo and RiemannLiouville sense, if we viewed them as a convolution. However, it is not always possible to find the power law behaviour in nature. In 2016 Abdon Atangana and Dumitru Baleanu proposed a derivative that is based upon the generalized Mittag-Leffler function, since the Mittag-Leffler function is more ...

As technology advances and the Internet makes our world a global village, it is important to understand prospective career of freelancing. A novel symmetric fractional mathematical model introduced in this study describe competitive market freelancing significance information its acceptance. In study, fixed point theory applied analyze uniqueness existence freelance model. Its numerical solutio...

Abstract In this paper, we obtain sufficient conditions for the existence and uniqueness results of pantograph fractional differential equations (FDEs) with nonlocal involving Atangana–Baleanu–Caputo (ABC) derivative operator orders. Our approach is based on reduction FDEs to integral some fixed point theorems such as Banach’s contraction principle theorem Krasnoselskii. Further, Gronwall’s ine...

In the present paper, we determine estimations on Atangana-Baleanu-Caputo fractional derivative at extreme points. With assistance of obtained, derive comparison results. Peano's type existence results established for nonlinear differential equations involving derivative. The acquired are then utilized to deal with local, extremal and global solution.

Recently, many fractional integral operators were introduced by different mathematicians. One of these operators, Atangana-Baleanu operator, was defined Atangana and Baleanu (Atangana Baleanu, 2016). In this study, firstly, a new identity using is proved. Then, inequalities have been obtained for convex concave functions with the help some certain inequalities.