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  1. Content type: Research

    This paper develops a Legendre neural network method (LNN) for solving linear and nonlinear ordinary differential equations (ODEs), system of ordinary differential equations (SODEs), as well as classic Emden–F...

    Authors: Yunlei Yang, Muzhou Hou and Jianshu Luo

    Citation: Advances in Difference Equations 2018 2018:469

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  2. Content type: Research

    Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The actio...

    Authors: Thabet Abdeljawad and Dumitru Baleanu

    Citation: Advances in Difference Equations 2018 2018:468

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  3. Content type: Research

    This paper concerns the asymptotic behavior of the solution to a class of coupled semilinear parabolic systems with gradient terms. The Fujita-type blow-up theorems are established and the critical Fujita curv...

    Authors: Guanming Gai, Qiang Liu, Yang Na and Mingjun Zhou

    Citation: Advances in Difference Equations 2018 2018:467

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  4. Content type: Research

    The construction of implicit Runge–Kutta–Nyström (RKN) method is considered in this paper. Based on the symmetric, symplectic, and exponentially fitted conditions, a class of implicit RKN integrators is obtain...

    Authors: Huai Yuan Zhai, Wen Juan Zhai and Bing Zhen Chen

    Citation: Advances in Difference Equations 2018 2018:463

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  5. Content type: Research

    In this paper, we present a stabilized lowest equal-order mixed finite element (FE) method for the Oseen viscoelastic fluid flow obeying an Oldroyd-B type constitutive law. To approximate the velocity, pressur...

    Authors: Shahid Hussain, Md. Abdullah Al Mahbub, Nasrin Jahan Nasu and Haibiao Zheng

    Citation: Advances in Difference Equations 2018 2018:461

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  6. Content type: Research

    In this paper, the investment process is modeled by backward stochastic differential equation. We investigate a necessary condition for optimal investment problem by the method of non-smooth analysis. Furtherm...

    Authors: Helin Wu, Yong Ren and Feng Hu

    Citation: Advances in Difference Equations 2018 2018:460

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  7. Content type: Research

    This paper is concerned with a class of two-term fractional differential equations. Three-point boundary value problems with mixed Riemann–Liouville fractional differential and integral boundary conditions are...

    Authors: Lei Xu, Qixiang Dong and Gang Li

    Citation: Advances in Difference Equations 2018 2018:458

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  8. Content type: Research

    In this paper, we give a generalization of normal curves to n-dimensional Euclidean space. Then we obtain a necessary and sufficient condition for a curve to be a normal curve in the n-dimensional Euclidean space...

    Authors: Özcan Bektaş

    Citation: Advances in Difference Equations 2018 2018:456

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  9. Content type: Research

    In this article, by using nonlinear Leray–Schauder-type alternative and Banach’s fixed point theorem, we investigate existence and uniqueness of solutions. We also prove Hyers–Ulam stability for the proposed c...

    Authors: Hasib Khan, Wen Chen, Aziz Khan, Tahir S. Khan and Qasem M. Al-Madlal

    Citation: Advances in Difference Equations 2018 2018:455

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  10. Content type: Research

    In this manuscript, we prove new aspects for several Opial-type integral inequalities for the left and right Caputo–Fabrizio operators with nonsingular kernel. For this purpose we use the inequalities obtained...

    Authors: Yasemin Başcı and Dumitru Baleanu

    Citation: Advances in Difference Equations 2018 2018:452

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  11. Content type: Research

    In this paper, a dynamic compartmental model is constructed for the transmission of HIV/AIDS receiving drug treatment and knowledge from effective awareness programs through media. Using stability theory of di...

    Authors: Priti Kumar Roy and Shubhankar Saha

    Citation: Advances in Difference Equations 2018 2018:451

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  12. Content type: Research

    In this paper, we propose a numerical scheme for a system of two linear singularly perturbed parabolic convection-diffusion equations. The presented numerical scheme consists of a classical backward-Euler sche...

    Authors: Li-Bin Liu, Guangqing Long and Yong Zhang

    Citation: Advances in Difference Equations 2018 2018:450

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  13. Content type: Research

    In this paper, we obtain two approximations in law of the complex fractional Brownian motion by processes constructed from a Poisson process and a Lévy process, respectively.

    Authors: Liheng Sang, Guangjun Shen and Qingbo Wang

    Citation: Advances in Difference Equations 2018 2018:444

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  14. Content type: Research

    A finite difference scheme, based upon the Crank–Nicolson scheme, is applied to the numerical approximation of a two-dimensional time fractional non-Newtonian fluid model. This model not only possesses a multi...

    Authors: Yanqin Liu, Xiuling Yin, Libo Feng and Hongguang Sun

    Citation: Advances in Difference Equations 2018 2018:442

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  15. Content type: Research

    In this paper, we define weak θ-contractions on a metric space into itself by extending θ-contractions introduced by Jleli and Samet (J. Inequal. Appl. 2014:38, 2014) and utilize the same to prove some fixed poin...

    Authors: Mohammad Imdad, Waleed M. Alfaqih and Idrees A. Khan

    Citation: Advances in Difference Equations 2018 2018:439

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  16. Content type: Research

    In this paper, we study the Hopf-zero bifurcation of Oregonator oscillator with delay. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, we get the normal form by per...

    Authors: Yuting Cai, Liqin Liu and Chunrui Zhang

    Citation: Advances in Difference Equations 2018 2018:438

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  17. Content type: Research

    In this paper, stabilization is studied for a two-dimensional delta operator system with time-varying delays and actuator saturation. Both lower and upper bounds of the time-varying delays are considered. An e...

    Authors: Dan Peng, Ting Zhang and Hongjiu Yang

    Citation: Advances in Difference Equations 2018 2018:437

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  18. Content type: Research

    This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and di...

    Authors: Nuchira Khongja, Thongchai Botmart, Piyapong Niamsup and Wajaree Weera

    Citation: Advances in Difference Equations 2018 2018:435

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  19. Content type: Research

    In this paper, we prove the existence and uniqueness of the equilibrium solution of the system by using the M-matrix and the topological degree technique and study the boundedness and robustness of dynamics of re...

    Authors: Ruofeng Rao and Shouming Zhong

    Citation: Advances in Difference Equations 2018 2018:434

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  20. Content type: Research

    In this paper, we consider a numerical solution for nonlinear advection–diffusion equation by a backward semi-Lagrangian method. The numerical method is based on the second-order backward differentiation formu...

    Authors: Soyoon Bak, Philsu Kim, Xiangfan Piao and Sunyoung Bu

    Citation: Advances in Difference Equations 2018 2018:432

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  21. Content type: Research

    In this paper, we introduce the concept of complete-closed time scales under translational and non-translational shifts and propose new definitions of special functions arising from dynamic equations on time s...

    Authors: Chao Wang, Ravi P. Agarwal, Donal O’Regan and Gaston M. N’Guérékata

    Citation: Advances in Difference Equations 2018 2018:429

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  22. Content type: Research

    In this paper, we formulate and study a mathematical model for the dynamics of jigger infestation incorporating public health education using systems of ordinary differential equations and computational simula...

    Authors: Rachel A. Nyang’inja, David N. Angwenyi, Cecilia M. Musyoka and Titus O. Orwa

    Citation: Advances in Difference Equations 2018 2018:426

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  23. Content type: Research

    This paper is devoted to an investigation of the multiple positive solutions to a class of infinite-point boundary value problems of nonlinear fractional differential equations coupled with the p-Laplacian ope...

    Authors: Han Wang, Suli Liu and Huilai Li

    Citation: Advances in Difference Equations 2018 2018:425

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  24. Content type: Research

    In this paper, we consider an efficient numerical algorithm for solving the two-dimensional fractional cable equation. The stability and convergency of the numerical scheme are rigorously proved by the Fourier...

    Authors: Ming Zhu Li, Li Juan Chen, Qiang Xu and Xiao Hua Ding

    Citation: Advances in Difference Equations 2018 2018:424

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  25. Content type: Research

    A three-species cooperative system with time delays and Lévy jumps is proposed in this paper. Firstly, by comparison method and inequality techniques, we discuss the stability in mean and extinction of species...

    Authors: Yuanfu Shao, Yuming Chen and Binxiang Dai

    Citation: Advances in Difference Equations 2018 2018:423

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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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