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  1. Content type: Research

    We solve a coupled system of nonlinear fractional differential equations equipped with coupled fractional nonlocal non-separated boundary conditions by using the Banach contraction principle and the Leray–Scha...

    Authors: Sabbavarapu Nageswara Rao and Meshari Alesemi

    Citation: Advances in Difference Equations 2019 2019:97

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  2. Content type: Research

    A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems. The methodology of the FRPS metho...

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

    Citation: Advances in Difference Equations 2019 2019:95

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  3. Content type: Research

    New exact solutions of the space–time conformable Caudrey–Dodd–Gibbon (CDG) equation have been derived by implementing the conformable derivative. The generalized Riccati equation mapping method is applied to ...

    Authors: Sadaf Bibi, Naveed Ahmed, Imran Faisal, Syed Tauseef Mohyud-Din, Muhammad Rafiq and Umar Khan

    Citation: Advances in Difference Equations 2019 2019:89

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  4. Content type: Research

    In this paper, we define a characteristic equation of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative. At the same time, by applying the Laplace transform and matrix ...

    Authors: Hong Li, Shou-ming Zhong, Jun Cheng and Hou-biao Li

    Citation: Advances in Difference Equations 2019 2019:86

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  5. Content type: Research

    It was found that the constitutive behaviour of granular soil was dependent on its density and pressure (i.e. material state). To capture such state dependence, a variety of state variables were empirically pr...

    Authors: Yifei Sun and Changjie Zheng

    Citation: Advances in Difference Equations 2019 2019:83

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  6. Content type: Research

    By using stochastic analysis, fractional analysis, compact semigroups and the Schauder fixed-point theorem, we discuss the approximate boundary controllability of a nonlocal Hilfer fractional stochastic differ...

    Authors: Hamdy M. Ahmed, Mahmoud M. El-Borai and M. Elsaid Ramadan

    Citation: Advances in Difference Equations 2019 2019:82

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  7. Content type: Research

    The phytoplankton–zooplankton is fundamentally important to study plankton and protect marine environment. In this paper, we propose a diffusive phytoplankton–zooplankton model, in which we also consider time ...

    Authors: Yanfeng Li, Haicheng Liu, Ruizhi Yang and Leiyu Tang

    Citation: Advances in Difference Equations 2019 2019:79

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  8. Content type: Research

    This paper is devoted to investigating the dynamics of a diffusive Leslie–Gower predator–prey system with ratio-dependent Holling III functional response. We first establish the stability of positive constant ...

    Authors: Xiaoyuan Chang and Jimin Zhang

    Citation: Advances in Difference Equations 2019 2019:76

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  9. Content type: Research

    In this paper, a high-order numerical scheme is proposed for solving the two-dimensional fractional reaction–subdiffusion equation. The method is based on adopting a third-order weighted and shifted Grünwald d...

    Authors: Xiaoyong Xu and Da Xu

    Citation: Advances in Difference Equations 2019 2019:75

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  10. Content type: Research

    In this paper, the concept of upper and lower solutions method combined with the fixed point theorem is used to investigate the existence of oscillatory and nonoscillatory solutions for a class of initial valu...

    Authors: Mouffak Benchohra, Samira Hamani and Yong Zhou

    Citation: Advances in Difference Equations 2019 2019:74

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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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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  16. 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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  17. 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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  18. 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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  19. 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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  20. 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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  21. 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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  22. 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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  23. 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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  24. 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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  25. 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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  26. 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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  27. 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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  28. 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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  29. 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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Editors-in-Chief

​​​​​​​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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