... 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...

... OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received November 10, 2017; final manuscript received July 31, 2018; published online September 10, 2018. Assoc. Editor: Dumitru Baleanu. 10 11 2017 31 07 2018 Fractional calculus Stability Time delay systems Over...

... 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...

... 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...

... . 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...

... 18, 2017; final manuscript received August 29, 2017; published online July 26, 2018. Assoc. Editor: Dumitru Baleanu. 18 07 2017 29 08 2017 Algorithms Fractional calculus Integration methods During the last several decades, fractional calculus has been developed very...

...; 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...

... saturation are utilized as illustrative examples. The feasibility of the proposed synchronization scheme is demonstrated through numerical simulations. Fractional calculus shares the same history as integer calculus, but it is not until recent decades that applications of fractional calculus have been...

...: a brief introduction to fractional calculus and coexistence of hidden attractors are discussed in Sec. 1 focusing on the motivation and novelty of the proposed work. Section 2 states the preliminaries of fractional calculus definitions, theorems, and computational schemes adopted. The proposed FOSs...

... future studies. 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...

...; 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 to noninteger order, was recognized...

... of the closed-loop system. However, despite fractional calculus provides with advanced properties for modeling and control of dynamical systems and real physical processes, the induced stability features are difficult to be inferred due to the memory and heritage inherent to the fractional-order operators. Thus...

..., 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...

... Sediment ,” J. Hydraul. Eng. , 129 ( 2 ), pp. 120 – 128 . 10.1061/(ASCE)0733-9429(2003)129:2(120) [12] Rossikhin , Y. A. , and Shitikova , M. V. , 1997 , “ Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids ,” ASME Appl. Mech...

... – 647 . 10.1002/rnc.1149 [13] Oldham , K. , and Spanier , J. , 1974 , The Fractional Calculus Theory and Applications of Differentiation and Integration...

... 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 calculus [ 1 ], which...

... Wang. 20 11 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...

... 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...