... for publication in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received February 18, 2018; final manuscript received August 22, 2018; published online September 17, 2018. Assoc. Editor: Bernard Brogliato. 18 02 2018 22 08 2018 Control Fractional calculus...

... Province, China (Grant No. DRA2015518). References [1] Podlubny , I. , 1999 , Fractional Differential Equations , Academic Press , San Diego, CA . [2] Magin , R. L. , 2004 , “ Fractional Calculus in Bioengineering ,” Crit. Rev. Biomed. Eng. , 32 ( 2 ), pp. 1 – 104 . 10.1615...

... received July 11, 2018; published online August 27, 2018. Assoc. Editor: Dumitru Baleanu. 10 10 2017 11 07 2018 Algorithms Computational mechanics Fractional calculus Integration methods Fractional differential equations (FDEs) have drawn increasing attention and interest...

... . Manuscript received January 6, 2018; final manuscript received July 21, 2018; published online August 22, 2018. Assoc. Editor: Brian Feeny. 06 01 2018 21 07 2018 Algorithms Fractional calculus Nonlinear dynamical systems Numerical Integration methods Fractional differential...

... in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received April 23, 2018; final manuscript received July 31, 2018; published online August 22, 2018. Assoc. Editor: Dumitru Baleanu. 23 04 2018 31 07 2018 Algorithms Fractional calculus Nonlinear dynamical...

... Algorithms Fractional calculus Integration methods During the last several decades, fractional calculus has been developed very quickly due to its various applications in fields of engineering, mechanics, physics, economics, and biology; see Refs. [ 1 – 9 ]. It is known that there have existed...

... . Manuscript received June 13, 2017; final manuscript received March 11, 2018; published online July 26, 2018. Assoc. Editor: Themistoklis Sapsis. 13 06 2017 11 03 2018 Chaotic dynamics Control Fractional calculus Stability of nonlinear systems Fractional calculus shares...

... been studying the combined dynamics of coexisting hidden attractors as in Refs. [ 10 – 12 ] and [ 14 – 17 ]. However, such study reported so far in the literature is only confined to integer-order (IO) dynamics. Fractional calculus has seen a dramatic rise in engineering, biological and medical...

... 26, 2018. Assoc. Editor: Dumitru Baleanu. 10 08 2017 05 11 2017 Control Fractional calculus Stability of nonlinear systems The purpose of fractional calculus is to generalize standard derivatives into noninteger order operators. As well acknowledged in the literature...

.... National Natural Science Foundation of China (Grant Nos. 41030331, 11572356, and 11672337). References [1] Bagley , L. , and Torvik , J. , 1983 , “ A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity ,” J. Rheol. , 27 ( 3 ), pp. 201 – 210 . 10.1122...

...; final manuscript received May 15, 2018; published online June 18, 2018. Assoc. Editor: Dumitru Baleanu. 08 12 2017 15 05 2018 Algorithms Fractional calculus Numerical Integration methods Recently, fractional calculus (FC), the theory of differentiation and integration...

... With Rational Orders: A Survey ,” Fractional Calculus Appl. Anal. , 12 ( 3 ), pp. 269 – 298 . http://www.math.bas.bg/complan/fcaa/volume12/fcaa123/IvoPetras_FCAA_12_3.pdf [35] Li , Y. , Chen , Y. Q. , and Podlubny , I. , 2009 , “ Mittag-Leffler Stability of Fractional Order Nonlinear...

..., 2017; final manuscript received April 4, 2018; published online May 2, 2018. Assoc. Editor: Zaihua Wang. 27 11 2017 04 04 2018 Control Fractional calculus Nonlinear dynamical systems Time delay systems Stability of nonlinear systems Fractional calculus is a developed...

... 2017 25 03 2018 Fractional calculus Nonlinear dynamical systems Bed-load transport is one of the most complex hydrological processes whose nonlinear dynamics have not been fully understood and computational models have not been fully developed. Bed-load transport affects river...

... are illustrated through matlab simulations to demonstrate the usefulness of the introduced control technique. 1 Corresponding author. Control Fractional calculus Nonlinear dynamical systems Stability Stability of nonlinear systems Mechanical systems are generally subjected to various kinds...

.... 14 11 2017 06 03 2018 Algorithms Fractional calculus Design optimization Parameter estimation System identification Numerical Design sensitivity Nonlinear systems Integration methods During the past decades, much attention has been drawn for the study of fractional...

... ] investigated the bifurcation and resonance phenomena in a fractional Mathieu–Duffing oscillator with a fast parametric excitation and a slow external excitation. Fractional calculus Nonlinear oscillations Vibration 20 11 2017 01 03 2018 Contributed by the Design Engineering...

...; published online January 24, 2018. Assoc. Editor: Dumitru Baleanu. 20 09 2017 10 12 2017 Computational kinematics Fractional calculus Nonlinear dynamical systems Nonlinear oscillations Nonlinear phenomena Dynamics Vibration A weak signal can be amplified by nonlinear...

...Tran Minh Duc; Ngo Van Hoa; Thanh-Phong Dao This paper investigates a novel adaptive fuzzy fractional-order nonsingular terminal sliding mode controller (AFFO-NTSMC) for second-order nonlinear dynamic systems. The technique of fractional calculus and nonsingular terminal sliding mode control (NTSMC...

... September 19, 2016; final manuscript received November 6, 2017; published online January 10, 2018. Editor: Bala Balachandran. 19 09 2016 06 11 2017 Control Fractional calculus Nonlinear dynamical systems Nonlinear oscillations Stability Stability of nonlinear systems Vibration...