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  1. Content type: Research

    This paper is concerned with a kind of non-zero sum differential game driven by mean-field backward stochastic differential equation (MF-BSDE) with asymmetric information, whose novel feature is that both the ...

    Authors: Pengyan Huang, Guangchen Wang and Huanjun Zhang

    Citation: Advances in Difference Equations 2019 2019:236

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  2. Content type: Research

    In this paper, we explore a stochastic non-autonomous one-predator–two-prey system with Beddington–DeAngelis functional response and impulsive perturbations. First, by using Itô’s formula, exponential martinga...

    Authors: Haokun Qi, Xinzhu Meng and Tao Feng

    Citation: Advances in Difference Equations 2019 2019:235

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  3. Content type: Research

    The Mathieu series appeared in the study of elasticity of solid bodies in the work of Émile Leonard Mathieu. Since then numerous authors have studied various problems arising from the Mathieu series in several...

    Authors: Owais Khan, Nabiullah Khan, Dumitru Baleanu and Kottakkaran Sooppy Nisar

    Citation: Advances in Difference Equations 2019 2019:234

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  4. Content type: Research

    This work is an attempt at studying leader-following model on the arbitrary time scale. The step size is treated as a function of time. Our purpose is establishing conditions ensuring a leader-following consen...

    Authors: Ewa Schmeidel, Urszula Ostaszewska and Małgorzata Zdanowicz

    Citation: Advances in Difference Equations 2019 2019:231

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  5. Content type: Research

    In this paper, using the idea of separated intervals in non-instantaneous impulsive equations, we initiate the study of initial value problems for mixed-order ordinary and fractional differential equations wit...

    Authors: Suphawat Asawasamrit, Yasintorn Thadang, Sotiris K. Ntouyas and Jessada Tariboon

    Citation: Advances in Difference Equations 2019 2019:229

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  6. Content type: Research

    We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional deriva...

    Authors: Usman Riaz, Akbar Zada, Zeeshan Ali, Yujun Cui and Jiafa Xu

    Citation: Advances in Difference Equations 2019 2019:226

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  7. Content type: Research

    In this paper, we analyze the load deflection behavior of the superstructure elements of beam bridges under two different beam–beam connection designs. We present a mathematical model for beam–bridge structura...

    Authors: Doungporn Wiwatanapataphee, Nathnarong Khajohnsaksumeth and Yong Hong Wu

    Citation: Advances in Difference Equations 2019 2019:225

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  8. Content type: Research

    In this paper, we establish sixteen interesting generalized fractional integral and derivative formulas including their composition formulas by using certain integral transforms involving generalized

    Authors: Ravi P. Agarwal, Adem Kılıçman, Rakesh K. Parmar and Arjun K. Rathie

    Citation: Advances in Difference Equations 2019 2019:221

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  9. Content type: Research

    In this paper, we study the existence and uniqueness of solutions for two classes of boundary value problems for impulsive Caputo type fractional Hahn difference equations, by using the Banach contraction mapp...

    Authors: Jessada Tariboon, Sotiris K. Ntouyas and Bundit Sutthasin

    Citation: Advances in Difference Equations 2019 2019:220

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  10. Content type: Research

    Ultrashort pulse propagation in optical transmission lines and phenomena in particle physics can be investigated via the cubic–quintic Ginzburg–Landau equation and the Phi-4 equation, respectively. The main ob...

    Authors: Sekson Sirisubtawee, Sanoe Koonprasert, Surattana Sungnul and Takerngsak Leekparn

    Citation: Advances in Difference Equations 2019 2019:219

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  11. Content type: Research

    So far, mobility in fish population has not been given sufficient attention, although movement and spatial heterogeneity can be an important dynamic feature that plays a critical role in their exploitation. Ha...

    Authors: Chontita Rattanakul, Yongwimon Lenbury and Jeerawan Suksamran

    Citation: Advances in Difference Equations 2019 2019:218

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  12. Content type: Research

    We propose and study two finite difference schemes (FDSs) for the double dispersion equations. The first FDS is symplectic, while the second one preserves the discrete momentum exactly. Both FDS conserve the disc...

    Authors: Natalia Kolkovska and Veselina Vucheva

    Citation: Advances in Difference Equations 2019 2019:216

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  13. Content type: Research

    In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (F...

    Authors: Sajjad Ali, Thabet Abdeljawad, Kamal Shah, Fahd Jarad and Muhammad Arif

    Citation: Advances in Difference Equations 2019 2019:215

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  14. Content type: Review

    An oil spill is the release of liquid petroleum into the marine ecosystem leading to huge damages in the natural resources. Prediction of oil spill spreading can help in handling accidental oil spills. This st...

    Authors: Kittipong Srikhaetai, Kittisak Chayantrakom and Wattana Kanbua

    Citation: Advances in Difference Equations 2019 2019:214

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  15. Content type: Research

    In this paper, we establish modified Saigo fractional integral operators involving the product of a general class of multivariable polynomials and the multivariable H-function. The results established here are of...

    Authors: D. L. Suthar, Belete Debalkie and Mitku Andualem

    Citation: Advances in Difference Equations 2019 2019:213

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  16. Content type: Research

    This article aims to develop fractional order convolution theory to bring forth innovative methods for generating fractional Fourier transforms by having recourse to solutions for fractional difference equatio...

    Authors: Dumitru Baleanu, Maysaa Alqurashi, Meganathan Murugesan and Britto Antony Xavier Gnanaprakasam

    Citation: Advances in Difference Equations 2019 2019:212

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  17. Content type: Research

    In this paper, an optimal control for a novel fractional West Nile virus model with time delay is presented. The proposed model is governed by a system of fractional delay differential equations, where the fra...

    Authors: N. H. Sweilam, O. M. Saad and D. G. Mohamed

    Citation: Advances in Difference Equations 2019 2019:210

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  18. Content type: Research

    In this paper, four different forms of a model to describe the dynamics of autoimmune diseases (with emphasis on Guillain–Barré syndrome) are proposed. In the first two cases, the immune response is supposed t...

    Authors: Mohammed Fathy Elettreby, Elsayed Ahmed and Muntaser Safan

    Citation: Advances in Difference Equations 2019 2019:208

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  19. Content type: Research

    From the standpoint of fishery management, an essential component of the basic information upon which policy can be based consists of intelligence from field data and computations. In certain situations, these...

    Authors: Jeerawan Suksamran and Yongwimon Lenbury

    Citation: Advances in Difference Equations 2019 2019:205

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  20. Content type: Research

    In this paper, we expanded our computation to obtain a simpler and detailed reduction and normal form of a delayed reaction–diffusion differential system with Bogdanov–Takens (B–T) singularity. By using the ce...

    Authors: Longyue Li, Jianzhi Cao and Yingying Mei

    Citation: Advances in Difference Equations 2019 2019:204

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  21. Content type: Research

    Salinity refers to the amount of salt in rivers, where the salt can be in many different forms. There are two main methods of defining the concentration of salt in water such as the total dissolved solid measu...

    Authors: Pornpon Othata and Nopparat Pochai

    Citation: Advances in Difference Equations 2019 2019:203

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  22. Content type: Research

    Recently, extended r-central factorial numbers of the second kind and extended r-central Bell polynomials were introduced and various results of them were investigated. The purpose of this paper is to further der...

    Authors: Lee-Chae Jang, Taekyun Kim, Dae San Kim and Han Young Kim

    Citation: Advances in Difference Equations 2019 2019:202

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  23. Content type: Research

    In recent years, many new definitions of fractional derivatives have been proposed and used to develop mathematical models for a wide variety of real-world systems containing memory, history, or nonlocal effec...

    Authors: Elvin J. Moore, Sekson Sirisubtawee and Sanoe Koonprasert

    Citation: Advances in Difference Equations 2019 2019:200

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  24. Content type: Research

    This paper regards function matrix projective synchronization of two different non-dissipatively coupled complex dynamical networks for different dimensions and different nodes. In this kind of complex dynamic...

    Authors: Yanchao Shi, Xin Wang, Xiangyan Zeng and Yang Cao

    Citation: Advances in Difference Equations 2019 2019:198

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  25. Content type: Research

    In this article, we propose a novel fractional generalization of the three-dimensional differential transform method, namely the ternary-fractional differential transform method, that extends its applicability...

    Authors: Feras Yousef, Marwan Alquran, Imad Jaradat, Shaher Momani and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:197

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  26. Content type: Research

    This paper introduces the improved LS-SVM algorithms for solving two-point and multi-point boundary value problems of high-order linear and nonlinear ordinary differential equations. To demonstrate the reliabi...

    Authors: Yanfei Lu, Qingfei Yin, Hongyi Li, Hongli Sun, Yunlei Yang and Muzhou Hou

    Citation: Advances in Difference Equations 2019 2019:195

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  27. Content type: Research

    A class of stochastic Runge–Kutta–Nyström (SRKN) methods for the strong approximation of second-order stochastic differential equations (SDEs) are proposed. The conditions for strong convergence global order 1...

    Authors: Qiang Ma, Yuanwei Song, Wei Xiao, Wendi Qin and Xiaohua Ding

    Citation: Advances in Difference Equations 2019 2019:192

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  28. Content type: Research

    In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Be...

    Authors: Dae San Kim, Han Young Kim, Sung-Soo Pyo and Taekyun Kim

    Citation: Advances in Difference Equations 2019 2019:190

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  29. Content type: Research

    This paper aims to present an application of the Riemann–Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrödinger equation arising in an optical fibe...

    Authors: Zhou-Zheng Kang, Tie-Cheng Xia and Wen-Xiu Ma

    Citation: Advances in Difference Equations 2019 2019:188

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  30. Content type: Research

    This paper proposes a stochastic three species food-chain model with harvesting and distributed delays. Some criteria for the global dynamics of all positive solutions, including the existence of global positi...

    Authors: Nafeisha Tuerxun, Zhidong Teng and Ahmadjan Muhammadhaji

    Citation: Advances in Difference Equations 2019 2019:187

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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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