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  1. Content type: Research

    To quickly solve the fractional Black–Scholes (B–S) equation in the option pricing problems, in this paper, we construct pure alternative segment explicit–implicit (PASE-I) and pure alternative segment implici...

    Authors: Yue Li, Xiaozhong Yang and Shuzhen Sun

    Citation: Advances in Difference Equations 2018 2018:280

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  2. Content type: Research

    In this paper, we study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we are going t...

    Authors: Taekyun Kim, Dae San Kim, Dmitry V. Dolgy and Jin-Woo Park

    Citation: Advances in Difference Equations 2018 2018:277

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  3. Content type: Research

    In this paper, we investigate a delayed differential algebraic prey–predator system, where commercial harvesting on predator and additive Allee effect on prey are considered. A discrete time delay is utilized ...

    Authors: Chao Liu, Luping Wang, Na Lu and Longfei Yu

    Citation: Advances in Difference Equations 2018 2018:278

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  4. Content type: Research

    This paper proposes and analyzes an efficient compact finite difference scheme for reaction–diffusion equation in high spatial dimensions. The scheme is based on a compact finite difference method (cFDM) for t...

    Authors: Rongpei Zhang, Zheng Wang, Jia Liu and Luoman Liu

    Citation: Advances in Difference Equations 2018 2018:274

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  5. Content type: Research

    The purpose of this paper is to present a methodological procedure to estimate the parameters of the exponential Ornstein–Uhlenbeck process, also known as the Schwartz (J. Finance 52(3):923–973, 1997) one-factor ...

    Authors: Carlos Armando Mejía Vega

    Citation: Advances in Difference Equations 2018 2018:269

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  6. Content type: Research

    The analytical and solitary traveling solutions of the nonlinear complex fractional generalized Zakharov equations are investigated. The nonlinear complex fractional generalized Zakharov equations describe the...

    Authors: Dianchen Lu, Aly R. Seadawy and Mostafa M. A. Khater

    Citation: Advances in Difference Equations 2018 2018:266

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  7. Content type: Research

    In this paper, by combining graph theory with coincidence degree theory as well as Lyapunov functional method, sufficient conditions to guarantee the existence and global exponential stability of periodic solu...

    Authors: Zhengqiu Zhang and Jinde Cao

    Citation: Advances in Difference Equations 2018 2018:261

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  8. Content type: Research

    In this article, we investigate numerical solution of a class of multi-order fractional differential equations with error correction and convergence analysis. According to fractional differential definition in...

    Authors: Wei Han, Yi-Ming Chen, Da-Yan Liu, Xiao-Lin Li and Driss Boutat

    Citation: Advances in Difference Equations 2018 2018:253

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  9. Content type: Research

    In this paper, a new set of functions called fractional-order Euler functions (FEFs) is constructed to obtain the solution of fractional integro-differential equations. The properties of the fractional-order E...

    Authors: Yanxin Wang, Li Zhu and Zhi Wang

    Citation: Advances in Difference Equations 2018 2018:254

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  10. Content type: Research

    In this paper, we consider the almost sure stability of the delayed reaction–diffusion neural networks (RDNNs) with Markovian jump parameters and Dirichlet boundary conditions. By constructing new Lyapunov fun...

    Authors: Weiyuan Zhang and Junmin Li

    Citation: Advances in Difference Equations 2018 2018:248

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  11. Content type: Research

    A single species stage-structured system incorporating partial closure for the populations and non-selective harvesting is proposed and studied in this paper. Local and global stability property of the boundar...

    Authors: An Xiao and Chaoquan Lei

    Citation: Advances in Difference Equations 2018 2018:245

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  12. Content type: Research

    In this paper, the existence and uniqueness of solutions for a class of nonlinear integro-differential equations on unbounded domains in Banach spaces are established under more general conditions by construct...

    Authors: Peiguo Zhang and Xinan Hao

    Citation: Advances in Difference Equations 2018 2018:247

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  13. Content type: Research

    In this paper, we discuss a nonlinear fractional order boundary value problem with nonlocal Erdélyi–Kober and generalized Riemann–Liouville type integral boundary conditions. By using Mawhin continuation theor...

    Authors: Qiao Sun, Shuman Meng and Yujun Cui

    Citation: Advances in Difference Equations 2018 2018:243

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  14. Content type: Research

    We study the pattern generating mechanism of a generalized Gierer–Meinhardt model with diffusions. We show the existence and stability of the Hopf bifurcation for the corresponding kinetic system under certain co...

    Authors: Jinliang Wang, You Li and Xiaojie Hou

    Citation: Advances in Difference Equations 2018 2018:241

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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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