Extended Algorithms for Approximating Variable Order Fractional Derivatives with Applications

Caputo derivatives of fractional variable order: Numerical approximations

(2016) Dina Tavares et al.   Communications in Nonlinear Science and Numerical Simulation

On the control and stability of variable-order mechanical systems

(2016) J. Orosco et al.   NONLINEAR DYNAMICS

Numerical algorithm for the variable-order Caputo fractional functional differential equation

(2016) A. H. Bhrawy et al.   NONLINEAR DYNAMICS

An efficient cubic spline approximation for variable-order fractional differential equations with time delay

(2016) Shole Yaghoobi et al.   NONLINEAR DYNAMICS

Derivation, interpretation, and analog modelling of fractional variable order derivative definition

(2015) Dominik Sierociuk et al.   APPLIED MATHEMATICAL MODELLING

Second-order approximations for variable order fractional derivatives: Algorithms and applications

(2015) Xuan Zhao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical calculation of the left and right fractional derivatives

(2015) J. Tenreiro Machado   JOURNAL OF COMPUTATIONAL PHYSICS

A review of operational matrices and spectral techniques for fractional calculus

(2015) Ali H. Bhrawy et al.   NONLINEAR DYNAMICS

On the Recursive Fractional Variable-Order Derivative: Equivalent Switching Strategy, Duality, and Analog Modeling

(2014) Dominik Sierociuk et al.   CIRCUITS SYSTEMS AND SIGNAL PROCESSING

On development of fractional calculus during the last fifty years

(2013) J. A. Tenreiro Machado et al.   SCIENTOMETRICS

An expansion formula for fractional derivatives of variable order

(2013) Teodor Atanackovic et al.   Open Physics

HOW TO APPROXIMATE THE FRACTIONAL DERIVATIVE OF ORDER 1 < α ≤ 2

(2012) ERCILIA SOUSA   INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

On the variable order dynamics of the nonlinear wake caused by a sedimenting particle

(2011) Lynnette E.S. Ramirez et al.   PHYSICA D-NONLINEAR PHENOMENA

Recent history of fractional calculus

(2010) J. Tenreiro Machado et al.   Communications in Nonlinear Science and Numerical Simulation

Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation

(2010) Chang-Ming Chen et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Variable-order fractional derivatives and their numerical approximations

(2010) Duarte Valério et al.   SIGNAL PROCESSING

Fractional and Hypersingular Operators in Variable Exponent Spaces on Metric Measure Spaces

(2009) Alexandre Almeida et al.   Mediterranean Journal of Mathematics

Variable-order fractional differential operators in anomalous diffusion modeling

(2009) HongGuang Sun et al.   PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

On mean square displacement behaviors of anomalous diffusions with variable and random orders

(2009) HongGuang Sun et al.   PHYSICS LETTERS A

Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term

(2009) P. Zhuang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere

(2008) H.T.C. Pedro et al.   JOURNAL OF VIBRATION AND CONTROL

Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation

(2008) G. Diaz et al.   NONLINEAR DYNAMICS