... 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...

... Project of Jiangsu 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...

... fractional-order proportional–integral control. Lorenzo and Hartley [ 11 ] applied the distributed-order fractional derivatives to study the rheological properties of composite materials. Lazovic et al. [ 25 ] utilized electrical impedance measurement data and distributed-order fractional calculus to model...

... . 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...

... 07 2017 29 08 2017 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...

...; published online July 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...

... 2018 Chaotic dynamics Control Fractional calculus Stability of nonlinear systems Fractional calculus shares the same history as integer calculus, but it is not until recent decades that applications of fractional calculus have been explored. In recent days, numerous literatures have...

.... Assoc. Editor: Dumitru Baleanu. 01 08 2017 21 03 2018 Bifurcations Chaotic dynamics Control Fractional calculus Nonlinear dynamical systems Nonlinear phenomena Stability of nonlinear systems The term “hidden attractor” was coined by Leonov et al. who discovered...

... OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received August 29, 2017; final manuscript received May 10, 2018; published online June 18, 2018. Assoc. Editor: Anindya Chatterjee. 29 08 2017 10 05 2018 Algorithms Fractional calculus Nonlinear dynamical systems...

... Baleanu. 08 12 2017 15 05 2018 Algorithms Fractional calculus Numerical Integration methods Recently, fractional calculus (FC), the theory of differentiation and integration to noninteger order, was recognized to describe accurately many fundamental problems in science...

... manuscript received April 30, 2018; published online May 30, 2018. Assoc. Editor: Zaihua Wang. 31 01 2018 30 04 2018 Control Fractional calculus Non-smooth dynamics Nonlinear dynamical systems Stability Stability of nonlinear systems In engineering practice...

..., 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...

... April 18, 2018. Assoc. Editor: Zaihua Wang. 30 11 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...

... . Manuscript received September 7, 2017; final manuscript received March 7, 2018; published online April 2, 2018. Assoc. Editor: Bernard Brogliato. 07 09 2017 07 03 2018 Control Fractional calculus Nonlinear dynamical systems Stability...

... and numerical methods [ 17 – 20 ] have been raised to solve the fractional order differential equations. Accordingly, it is also quite necessary to extend these basic results to fractional-order chaotic systems. During the past decades, much attention has been drawn for the study of fractional calculus [ 1...

... 2017 01 03 2018 Fractional calculus Nonlinear oscillations Vibration With the development of fractional-order calculus theory [ 1 – 4 ], the dynamics analysis of systems with fractional-order derivative [ 5 – 10 ] or fractional-order proportional–integral–derivative controller...

... manuscript received December 10, 2017; 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...

...Jian Yuan; Youan Zhang; Jingmao Liu; Bao Shi Fractional calculus is viewed as a novel and powerful tool to describe the stress and strain relations in viscoelastic materials. Consequently, the motions of engineering structures incorporated with viscoelastic dampers can be described by fractional...

...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...