New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations

Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system

(2018) K. M. Saad   European Physical Journal Plus

Finite Difference/Collocation Method for a Generalized Time-Fractional KdV Equation

(2018) Wen Cao et al.   Applied Sciences-Basel

Atangana–Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study

(2017) Arshad Khan et al.   Entropy

A new analysis for fractional model of regularized long-wave equation arising in ion acoustic plasma waves

(2017) Devendra Kumar et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

A new fractional operator of variable order: Application in the description of anomalous diffusion

(2017) Xiao-Jun Yang et al.   PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat transfer problems

(2017) Xiao-Jun Yang   Thermal Science

General fractional-order anomalous diffusion with non-singular power-law kernel

(2017) Xiao-Jun Yang et al.   Thermal Science

General fractional calculus operators containing the generalized Mittag-Leffler functions applied to anomalous relaxation

(2017) Xiaojun Yang   Thermal Science

On linear viscoelasticity within general fractional derivatives without singular kernel

(2017) Feng Gao et al.   Thermal Science

Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction–diffusion systems

(2017) Kolade M. Owolabi et al.   computational and applied mathematics

New discretization of Caputo–Fabrizio derivative

(2017) Tuğba Akman et al.   computational and applied mathematics

On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation

(2016) Abdon Atangana   APPLIED MATHEMATICS AND COMPUTATION

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation

(2016) Xiao-Jun Yang et al.   CHAOS

Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model

(2016) Obaid Jefain Julaighim Algahtani   CHAOS SOLITONS & FRACTALS

A new method for exact solutions of variant types of time-fractional Korteweg-de Vries equations in shallow water waves

(2016) S. Sahoo et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model

(2016) Abdon Atangana et al.   Thermal Science

A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations

(2015) A. H. Bhrawy et al.   CALCOLO

Analysis of the Keller–Segel Model with a Fractional Derivative without Singular Kernel

(2015) Abdon Atangana et al.   Entropy

Approximate analytical solution of the nonlinear fractional KdV–Burgers equation: A new iterative algorithm

(2015) Ahmad El-Ajou et al.   JOURNAL OF COMPUTATIONAL PHYSICS