Synchronization of a class of fractional-order neural networks with multiple time delays by comparison principles

School of Mathematics and Computational Science, Anqing Normal University, AnQing 246011, China wwzhahu@aliyun.com School of Mathematics, Anhui University, Hefei 230039, China rcwu@ahu.edu.cn School of Mathematics, Southeast University, Nanjing 210096, China jdcao@seu.edu.cn Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia aalsaedi@hotmail.com Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan tahaksag@yahoo.com

[1]  I. Podlubny Fractional differential equations , 1998 .

[2]  N. Laskin Fractional quantum mechanics and Lévy path integrals , 1999, hep-ph/9910419.

[3]  P. Butzer,et al.  AN INTRODUCTION TO FRACTIONAL CALCULUS , 2000 .

[4]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[5]  E. Ahmed,et al.  On fractional order differential equations model for nonlocal epidemics , 2007, Physica A: Statistical Mechanics and its Applications.

[6]  Jinde Cao,et al.  Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects , 2010 .

[7]  Elif Demirci,et al.  A fractional order SEIR model with vertical transmission , 2011, Math. Comput. Model..

[8]  Xiaodi Li,et al.  Lag synchronization of chaotic delayed neural networks via impulsive control , 2012, IMA Journal of Mathematical Control and Information.

[9]  Jinde Cao,et al.  Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems , 2013 .

[10]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[11]  I. Stamova Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays , 2014, Nonlinear Dynamics.

[12]  Zhigang Zeng,et al.  Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks , 2014, Neural Networks.

[13]  R. Rakkiyappan,et al.  Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays , 2015 .

[14]  Jinde Cao,et al.  Adaptive synchronization of fractional-order memristor-based neural networks with time delay , 2015, Nonlinear Dynamics.

[15]  Manfeng Hu,et al.  Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control , 2015 .

[16]  Liping Chen,et al.  Comparison principles and stability of nonlinear fractional-order cellular neural networks with multiple time delays , 2015, Neurocomputing.

[17]  Jinde Cao,et al.  Stability and synchronization of memristor-based fractional-order delayed neural networks , 2015, Neural Networks.

[18]  Jinde Cao,et al.  Projective synchronization of fractional-order memristor-based neural networks , 2015, Neural Networks.

[19]  Manuel A. Duarte-Mermoud,et al.  Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[20]  Jinde Cao,et al.  Finite-time synchronization of fractional-order memristor-based neural networks with time delays , 2016, Neural Networks.

[21]  Jinde Cao,et al.  Exponential H∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities , 2016, Science China Technological Sciences.

[22]  Jinde Cao,et al.  Synchronization of fractional-order complex-valued neural networks with time delay , 2016, Neural Networks.

[23]  Hu Wang,et al.  Synchronization for fractional-order time-delayed memristor-based neural networks with parameter uncertainty , 2016, J. Frankl. Inst..

[24]  Jinde Cao,et al.  Fixed-time synchronization of delayed memristor-based recurrent neural networks , 2017, Science China Information Sciences.

[25]  Xiaodi Li,et al.  Stability of nonlinear differential systems with state-dependent delayed impulses , 2016, Autom..

[26]  Xiaodi Li,et al.  Stabilization of Delay Systems: Delay-Dependent Impulsive Control , 2017, IEEE Transactions on Automatic Control.

[27]  Xiaoli Zhang,et al.  Effect of delayed impulses on input-to-state stability of nonlinear systems , 2017, Autom..

[28]  Jinde Cao,et al.  Bifurcations in a delayed fractional complex-valued neural network , 2017, Appl. Math. Comput..