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  1. 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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  2. 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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  3. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. Content type: Research

    We confirm the study (Licht in C. R., Méc. 341:697–700, 2013) devoted to the quasi-static response for a visco-elastic Kelvin–Voigt plate whose thickness goes to zero. For each thickness parameter, the quasi-stat...

    Authors: Yotsawat Terapabkajornded, Somsak Orankitjaroen and Christian Licht

    Citation: Advances in Difference Equations 2019 2019:186

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  9. Content type: Research

    This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discret...

    Authors: Muhammad Amin, Muhammad Abbas, Muhammad Kashif Iqbal and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:183

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  10. Content type: Research

    In this paper, we investigate the effect of insecticide on the population dynamics of brown planthoppers (a major insect pest of rice) and Cyrtorhinus lividipennis (one of the natural enemies of brown planthopper...

    Authors: Inthira Chaiya and Chontita Rattanakul

    Citation: Advances in Difference Equations 2019 2019:182

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  11. Content type: Research

    In this paper, a model of discrete delayed quaternion-valued neural networks with interval parameter uncertainties is considered. Some sufficient conditions for the existence, uniqueness and globally robust st...

    Authors: Xiaodong Wang, Jielin Zhou, Xiaofeng Chen and Yuanshun Tan

    Citation: Advances in Difference Equations 2019 2019:181

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  12. Content type: Research

    This paper is concerned with the problem of bifurcation for a ring fractional Hopfield neural network with leakage time delay and communication time delay. The stability and the Hopf bifurcations of such a net...

    Authors: Zhouhong Li, Chengdai Huang and Yuan Zhang

    Citation: Advances in Difference Equations 2019 2019:179

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  13. Content type: Research

    This manuscript deals with fractional differential equations including Caputo–Fabrizio differential operator. The conditions for existence and uniqueness of solutions of fractional initial value problems is es...

    Authors: Amjad Shaikh, Asifa Tassaddiq, Kottakkaran Sooppy Nisar and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:178

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  14. Content type: Research

    In this paper, an efficient finite element scheme is presented for a class of fourth-order nonlinear parabolic problems with variable coefficient. To deal with second-order term in weak formulation, we choose ...

    Authors: Dandan Qin, Yanwei Du, Bo Liu and Wenzhu Huang

    Citation: Advances in Difference Equations 2019 2019:175

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  15. Content type: Research

    To achieve synchronization of uncertain fractional-order chaotic systems with time-delays, an adaptive fuzzy controller with integer-order parameter adaptive laws, is established. Unknown nonlinear functions a...

    Authors: Xiaoli Qin, Shenggang Li and Heng Liu

    Citation: Advances in Difference Equations 2019 2019:174

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  16. Content type: Research

    In this paper, we consider a special, but important class of one-dimensional coupled map lattices, namely, in which the local dynamics including logistic map as a prototype possesses a snap-back repeller. For ...

    Authors: Lili Wei and Chenxing Zhou

    Citation: Advances in Difference Equations 2019 2019:172

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  17. Content type: Research

    Algae are fast growing microorganisms and beneficial in many ways, especially concerning food supplement, alternative energy, and wastewater treatment. Naturally, they need a light:dark regime for productive p...

    Authors: Sutamas Satthong, Kritsana Saego, Pongpatai Kitrungloadjanaporn, Narin Nuttavut, Somkid Amornsamankul and Wannapong Triampo

    Citation: Advances in Difference Equations 2019 2019:170

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  18. Content type: Research

    In this paper, we consider a delayed Hopfield two-neural system with a monotonic activation function and find the periodic coexistence by bifurcation analysis. Firstly, we obtain the pitchfork bifurcation of t...

    Authors: Zigen Song, Weiguo Qian, Bin Zhen and Xianghong Kong

    Citation: Advances in Difference Equations 2019 2019:167

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  19. Content type: Research

    In this manuscript, we talk over the existence of solutions of a class of hybrid Caputo–Hadamard fractional differential inclusions with Dirichlet boundary conditions. Our results are based on the Arzelá–Ascol...

    Authors: Mohammad Esmael Samei, Vahid Hedayati and Shahram Rezapour

    Citation: Advances in Difference Equations 2019 2019:163

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  20. Content type: Research

    In this paper, we investigate sums of finite products of Chebyshev polynomials of the first kind and those of Lucas polynomials. We express each of them as linear combinations of Hermite, extended Laguerre, Le...

    Authors: Taekyun Kim, Dae San Kim, Lee-Chae Jang and D. V. Dolgy

    Citation: Advances in Difference Equations 2019 2019:162

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  21. Content type: Research

    Volterra integro-differential equations arise in the modeling of natural systems where the past influence the present and future, for example pollution, population growth, mechanical systems and financial mark...

    Authors: Sami Ullah Khan, Mushtaq Ali and Ishtiaq Ali

    Citation: Advances in Difference Equations 2019 2019:161

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  22. Content type: Research

    In this paper, we mainly consider the existence and finite-time stability of solutions for a kind of ψ-Hilfer fractional differential equations involving time-varying delays and non-instantaneous impulses. By Sch...

    Authors: Danfeng Luo and Zhiguo Luo

    Citation: Advances in Difference Equations 2019 2019:155

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  23. Content type: Research

    One of the interesting fractional integro-differential equations is the three step crisis equation which has been reviewed recently. In this paper, we investigate the existence of solutions for a three step cr...

    Authors: Dumitru Baleanu, Khadijeh Ghafarnezhad and Shahram Rezapour

    Citation: Advances in Difference Equations 2019 2019:153

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  24. Content type: Research

    This paper is dedicated to Opial-type inequalities for arbitrary kernels using convex functions. These inequalities are further applied to a power function. Applications of the presented results are studied in...

    Authors: G. Farid, A. U. Rehman, S. Ullah, A. Nosheen, M. Waseem and Y. Mehboob

    Citation: Advances in Difference Equations 2019 2019:152

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  25. Content type: Research

    In this paper an SIR deterministic mathematical model for co-infection of pneumonia and meningitis is proposed. We use a seven compartment model by using ordinary differential equations. The positivity of futu...

    Authors: Getachew Teshome Tilahun

    Citation: Advances in Difference Equations 2019 2019:149

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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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