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  1. Content type: Research

    In this paper, we consider the flocking problem for a discrete Cucker–Smale model with packet loss. For describing the packet loss process, a more general condition including four different cases is adopted in...

    Authors: Ru Wang, Zheng Fang and Li Li

    Citation: Advances in Difference Equations 2019 2019:71

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  2. Content type: Research

    The Caputo fractional version of the generalized Newell–Whitehead–Segel model is considered. We introduced a numerical scheme to solve analytically the proposed application. We updated the style of the general...

    Authors: Mohammed Ali, Marwan Alquran and Imad Jaradat

    Citation: Advances in Difference Equations 2019 2019:70

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  3. Content type: Research

    The exact solutions of the Riemann problem for a symmetric system of Keyfitz–Kranzer type are obtained in fully explicit forms. Furthermore, the global solutions of the double Riemann problems are also constru...

    Authors: Pengyan Wang, Chun Shen and Xiuli Lin

    Citation: Advances in Difference Equations 2019 2019:69

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  4. Content type: Research

    In this paper, for a class of linear networked iterative learning control (ILC) systems, methods to compensate dropped input data in time or iteration domain are compared. Specifically, the transition matrices...

    Authors: Lixun Huang, Hanqing Ding, Zhe Zhang, Qiuwen Zhang and Lijun Sun

    Citation: Advances in Difference Equations 2019 2019:68

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  5. Content type: Research

    In this paper, we introduce a new numerical method for pricing American-style options, which has long been considered as a very challenging problem in financial engineering. Based on the HODIE (high order via ...

    Authors: Zhongdi Cen and Wenting Chen

    Citation: Advances in Difference Equations 2019 2019:67

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  6. Content type: Research

    So far, there are no any publications for solving and obtaining a numerical solution of Volterra integro-differential equations in the complex plane by using the finite element method. In this work, we use the...

    Authors: M. Erfanian and H. Zeidabadi

    Citation: Advances in Difference Equations 2019 2019:62

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  7. Content type: Research

    The dynamics of the osteoporotic bone turnover is studied in this paper with the aid of stability analysis of the associated mathematical model. Osteoporosis, which is a common bone disorder, is studied in thi...

    Authors: Sana Javed, Muhammad Younas, M. Yousaf Bhatti, Ayesha Sohail and Abdul Sattar

    Citation: Advances in Difference Equations 2019 2019:61

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  8. Content type: Research

    In this paper, the diffraction problem of periodic strip gratings is considered. The previous study of this problem usually concentrated on the numerical method; however, we try to analyze this problem and the...

    Authors: Enxi Zheng and Yujie Wang

    Citation: Advances in Difference Equations 2019 2019:60

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  9. Content type: Research

    For discrete-time iterative learning control systems, the discrete Fourier transform (DFT) is a powerful technique for frequency analysis, and Toeplitz matrices are a typical tool for the system input–output t...

    Authors: Xiaohui Li and Xiaoe Ruan

    Citation: Advances in Difference Equations 2019 2019:59

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  10. Content type: Research

    In this paper, we mainly give the Lie algebras E, F and H of three kinds and their commutator, respectively. Next, we establish three isospectral problems with the help of their corresponding loop algebras , ,...

    Authors: Yuan Wei, Li Yin and Xin Long

    Citation: Advances in Difference Equations 2019 2019:58

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  11. Content type: Research

    In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann–Liouville fractional integral supplemented with nonlocal ...

    Authors: Bashir Ahmad, Ahmed Alsaedi and Sara Salem

    Citation: Advances in Difference Equations 2019 2019:57

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  12. Content type: Research

    The primary motivation of this paper is to extend the application of the reproducing-kernel method (RKM) and the residual power series method (RPSM) to conduct a numerical investigation for a class of boundary...

    Authors: Shatha Hasan, Mohammed Al-Smadi, Asad Freihet and Shaher Momani

    Citation: Advances in Difference Equations 2019 2019:55

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  13. Content type: Research

    Any random model represents an action where uncertainty is present. In this article, we investigate a random process solution of the random convection–diffusion model using the finite difference technique. Add...

    Authors: M. A. Sohaly

    Citation: Advances in Difference Equations 2019 2019:54

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  14. Content type: Research

    In this paper, the robust optimal filtering problem is discussed for time-varying networked systems with randomly occurring quantized measurements via the variance-constrained method. The stochastic nonlineari...

    Authors: Chaoqing Jia and Jun Hu

    Citation: Advances in Difference Equations 2019 2019:53

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  15. Content type: Research

    In this paper, we present results on the existence, uniqueness, and Ulam–Hyers–Mittag-Leffler stability of solutions to a class of ψ-Hilfer fractional-order delay differential equations. We use the Picard operato...

    Authors: Kui Liu, JinRong Wang and Donal O’Regan

    Citation: Advances in Difference Equations 2019 2019:50

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  16. Content type: Research

    In this paper, a new generalized exponential rational function method is employed to extract new solitary wave solutions for the Zakharov–Kuznetsov equation (ZKE). The ZKE exhibits the behavior of weakly nonli...

    Authors: Behzad Ghanbari, Abdullahi Yusuf, Mustafa Inc and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:49

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  17. Content type: Research

    This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of...

    Authors: Nannan Ma, Zhibin Liu and Lin Chen

    Citation: Advances in Difference Equations 2019 2019:48

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  18. Content type: Research

    In this paper, we suggest a new exponential implicit method based on full step discretization of order four for the solution of quasilinear elliptic partial differential equation of the form ...

    Authors: R. K. Mohanty, Geetan Manchanda and Arshad Khan

    Citation: Advances in Difference Equations 2019 2019:47

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  19. Content type: Research

    We investigate the existence and uniqueness of a solution for a Sturm–Liouville fractional differential equation with a multi-point boundary condition via the Caputo derivative; existence and uniqueness result...

    Authors: Ahmed M. A. El-Sayed and Fatma M. Gaafar

    Citation: Advances in Difference Equations 2019 2019:46

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  20. Content type: Research

    This paper is concerned with the random exponential attractor for second order non-autonomous stochastic lattice system with multiplicative white noise and unbounded nonlinearity. Firstly, we transfer the stoc...

    Authors: Haijuan Su, Shengfan Zhou and Luyao Wu

    Citation: Advances in Difference Equations 2019 2019:45

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  21. Content type: Research

    In this paper, we study a stage-structured predator–prey model incorporating refuge for prey and additional food for predator. By analyzing the corresponding characteristic equations, we investigate the local ...

    Authors: Yuzhen Bai and Yunyun Li

    Citation: Advances in Difference Equations 2019 2019:42

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  22. Content type: Research

    In a recent paper several periodic systems of difference equations have been presented. We show in an elegant way that all the results therein follow from some known ones. We also show how some extensions of t...

    Authors: Stevo Stević, Bratislav Iričanin, Witold Kosmala and Zdeněk Šmarda

    Citation: Advances in Difference Equations 2019 2019:39

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  23. Content type: Research

    We study an epidemic model with nonlinear incidence rate, describing the saturated mass action and the psychological effect of certain serious diseases on the community. Firstly, the existence and local stabil...

    Authors: Ruixia Yuan, Zhidong Teng and Jinhui Li

    Citation: Advances in Difference Equations 2019 2019:37

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  24. Content type: Research

    In this paper, we study the nonlocal boundary value problem for a nonlinear fractional differential coupled system with fractional order impulses. Applying Nonlinear Alternative of Leray–Schauder, we obtain so...

    Authors: Kaihong Zhao and Hui Huang

    Citation: Advances in Difference Equations 2019 2019:36

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  25. Content type: Research

    It is well known that the drug treatment is always combined with the injection of immune factors. In this paper, a virus infection model with state-dependent impulsive control is considered. Firstly, by derivi...

    Authors: Huilan Wang, Binxiang Dai and Qizhen Xiao

    Citation: Advances in Difference Equations 2019 2019:35

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  26. Content type: Research

    This article represents a numerical analysis for a stochastic dengue epidemic model with incubation period of virus. We discuss the comparison of solutions between the stochastic dengue model and a determinist...

    Authors: Ali Raza, Muhammad Shoaib Arif and Muhammad Rafiq

    Citation: Advances in Difference Equations 2019 2019:32

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  27. Content type: Research

    In this paper, we derive seed and 1-soliton solutions of the Q2 equation in the Adler–Bobenko–Suris list. The seed solutions of Q2 are obtained using those of http://static-content.springer.com/image/art%3A10.1186%2Fs13662-019-1977-8/13662_2019_1977_Article_IEq1.gif ...

    Authors: Qiang Cheng, Cheng Zhang, Danda Zhang and Da-jun Zhang

    Citation: Advances in Difference Equations 2019 2019:30

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  28. Content type: Research

    The dynamical behavior of the predator–prey system is influenced effectively due to the mutual interaction of parasites. Regulations are imposed on biodiversity due to such type of interaction. With implementa...

    Authors: Waqas Ishaque, Qamar Din, Muhammad Taj and Muhammad Asad Iqbal

    Citation: Advances in Difference Equations 2019 2019:28

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  29. Content type: Research

    In this paper, we consider the extended central factorial polynomials and numbers of the second kind, and investigate some properties and identities for these polynomials and numbers. In addition, we give some...

    Authors: Taekyun Kim, Dae San Kim, Gwan-Woo Jang and Jongkyum Kwon

    Citation: Advances in Difference Equations 2019 2019:24

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Editors-in-Chief

agarwal_edit Ravi Agarwal, Texas A&M University, Kingsville, United States of America | 

Ravi's SpringerNature Publications

​​​​​​​mbnk_edit Martin Bohner, Missouri University of Science and Technology, United States of America | 

Martin's SpringerNature Publications

Elena_Braverman_image_edit Elena Braverman, University of Calgary Canada | 

Elena's SpringerNature Publications

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