New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications

Updating the state of the art of Nonlinear Dynamics and Complexity

(2016) Juan L.G. Guirao et al.   CHAOS SOLITONS & FRACTALS

Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order

(2016) Abdon Atangana et al.   CHAOS SOLITONS & FRACTALS

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

(2016) Obaid Jefain Julaighim Algahtani   CHAOS SOLITONS & FRACTALS

Analysis of non-homogeneous heat model with new trend of derivative with fractional order

(2016) Badr Saad T. Alkahtani et al.   CHAOS SOLITONS & FRACTALS

Triple pendulum model involving fractional derivatives with different kernels

(2016) A. Coronel-Escamilla et al.   CHAOS SOLITONS & FRACTALS

Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels

(2016) José Gómez-Aguilar et al.   Entropy

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

(2016) Abdon Atangana et al.   Thermal Science

Extinction for a discrete competition system with the effect of toxic substances

(2016) Qin Yue   Advances in Difference Equations

Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus

(2016) Abdon Atangana   European Physical Journal Plus

A weighted finite difference method for the fractional diffusion equation based on the Riemann–Liouville derivative

(2015) Ercília Sousa et al.   APPLIED NUMERICAL MATHEMATICS

New model of groundwater flowing within a confine aquifer: application of Caputo-Fabrizio derivative

(2015) Abdon Atangana et al.   Arabian Journal of Geosciences

Tempered fractional calculus

(2015) Farzad Sabzikar et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Invariant analysis of nonlinear fractional ordinary differential equations with Riemann–Liouville fractional derivative

(2015) T. Bakkyaraj et al.   NONLINEAR DYNAMICS

Forced oscillation of nonlinear fractional differential equations with damping term

(2015) Jichen Yang et al.   Advances in Difference Equations

Complexity and the Fractional Calculus

(2013) Pensri Pramukkul et al.   Advances in Mathematical Physics

Fractional-order Legendre functions for solving fractional-order differential equations

(2012) S. Kazem et al.   APPLIED MATHEMATICAL MODELLING

Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative

(2011) Trifce Sandev et al.   Journal of Physics A-Mathematical and Theoretical

Extension of gamma, beta and hypergeometric functions

(2010) Emine Özergin et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Some generating relations for extended hypergeometric functions via generalized fractional derivative operator

(2010) M. Ali̇ Özarslan et al.   MATHEMATICAL AND COMPUTER MODELLING