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  1. In this paper, we study an inverse source problem for the Rayleigh–Stokes problem for a generalized second-grade fluid with a fractional derivative model. The problem is severely ill-posed in the sense of Hada...

    Authors: Tran Thanh Binh, Hemant Kumar Nashine, Le Dinh Long, Nguyen Hoang Luc and Can Nguyen

    Citation: Advances in Difference Equations 2019 2019:331

    Content type: Research

    Published on:

  2. We consider analytic and formal solutions of certain family of q-difference-differential equations under the action of a complex perturbation parameter. The previous study (Lastra and Malek in Adv. Differ. Equ. 2...

    Authors: Thomas Dreyfus, Alberto Lastra and Stéphane Malek

    Citation: Advances in Difference Equations 2019 2019:326

    Content type: Review

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  3. A new class of 2m-point non-stationary subdivision schemes (SSs) is presented, including some of their important properties, such as continuity, curvature, torsion monotonicity, and convexity preservation. The mu...

    Authors: Abdul Ghaffar, Zafar Ullah, Mehwish Bari, Kottakkaran Sooppy Nisar, Maysaa M. Al-Qurashi and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:325

    Content type: Research

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  4. In this paper, the dynamics of a discrete market share attraction model are investigated. It shows that the system can undergo flip bifurcation and chaos. The stability and bifurcation of a market share attrac...

    Authors: Xiuqin Yang, Feng Liu, Qingyi Wang and Hua O. Wang

    Citation: Advances in Difference Equations 2019 2019:324

    Content type: Research

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  5. This paper mainly focuses on solitary waves excited by topography with time-dependent variable coefficient. By making use of multiple scale expansion and multiple level approximation method, a variable coeffic...

    Authors: Juanjuan Ji, Lanfang Zhang, Longxue Wang, Shengping Wu and Lihua Zhang

    Citation: Advances in Difference Equations 2019 2019:320

    Content type: Research

    Published on:

  6. In this paper, we consider the initial-boundary value problem of the one-dimensional compressible viscous and heat-conductive Navier–Stokes equations with a reacting mixture. This model is used to describe the...

    Authors: Mingyu Zhang

    Citation: Advances in Difference Equations 2019 2019:319

    Content type: Research

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  7. This paper proposes a delayed fractional-order model of glucose–insulin interaction in the sense of the Caputo fractional derivative with incommensurate orders. This fractional-order model is developed from th...

    Authors: Natchapon Lekdee, Sekson Sirisubtawee and Sanoe Koonprasert

    Citation: Advances in Difference Equations 2019 2019:318

    Content type: Research

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  8. A discrete monotone iterative method is reported here to solve a space-fractional nonlinear diffusion–reaction equation. More precisely, we propose a Crank–Nicolson discretization of a reaction–diffusion syste...

    Authors: Salvador Flores, Jorge E. Macías-Díaz and Ahmed S. Hendy

    Citation: Advances in Difference Equations 2019 2019:317

    Content type: Research

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  9. In this paper, we aim to obtain the existence of at least three classical solutions for nonlinear impulsive problems neither adding superlinear or local sublinear conditions to nonlinear term at zero nor addin...

    Authors: Jian Liu, Zengqin Zhao, Wenguang Yu and Tongqian Zhang

    Citation: Advances in Difference Equations 2019 2019:316

    Content type: Research

    Published on:

  10. In the paper, some variants of Montgomery identity with the help of delta and nabla integrals are established which are useful to produce Montgomery identity involving alpha diamond integrals for function of t...

    Authors: Masud Ahmad, Khalid Mahmood Awan, Shehzad Hameed, Khuram Ali Khan and Ammara Nosheen

    Citation: Advances in Difference Equations 2019 2019:314

    Content type: Research

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  11. In this paper, we study n-variable mappings that are quartic in each variable. We show that the conditions defining such mappings can be unified in a single functional equation. Furthermore, we apply an alternati...

    Authors: Abasalt Bodaghi, Choonkil Park and Oluwatosin T. Mewomo

    Citation: Advances in Difference Equations 2019 2019:312

    Content type: Research

    Published on:

  12. In this paper, we investigate some new nonlinear dynamic integral inequalities containing integration on infinite interval on time scales, which provide explicit bounds on unknown functions. Our results not on...

    Authors: Haidong Liu, Cuiyuan Li and Feichao Shen

    Citation: Advances in Difference Equations 2019 2019:311

    Content type: Research

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  13. In this paper, we obtain necessary and sufficient conditions for oscillation of a fourth order dynamic equation on time scales with deviating arguments. We discuss the oscillation behavior of solutions for str...

    Authors: Yong Zhou, Jia Wei He, Bashir Ahmad and Ahmed Alsaedi

    Citation: Advances in Difference Equations 2019 2019:308

    Content type: Research

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  14. Since bifurcation makes it difficult to manage a paddy ecosystem, controlling bifurcation is an important management tool. In this paper, the stability and bifurcation control for a fractional order paddy ecos...

    Authors: Kun Zheng, Xiaoli Zhou, Zhaohua Wu, Zhiming Wang and Tiejun Zhou

    Citation: Advances in Difference Equations 2019 2019:307

    Content type: Research

    Published on:

  15. One of the important mechanisms of the oil weathering processes (OWP) is spreading of oil spills. This mechanism is the horizontal expansion of the oil slick with inertia-gravity, gravity-viscosity, and viscou...

    Authors: Polapat Khlongkhoi, Kittisak Chayantrakom and Wattana Kanbua

    Citation: Advances in Difference Equations 2019 2019:306

    Content type: Research

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  16. This paper presents the development of a new iterative method for solving the two-dimensional hyperbolic telegraph fractional differential equation (2D-HTFDE) which is central to the mathematical modeling of t...

    Authors: Ajmal Ali and Norhashidah Hj. Mohd. Ali

    Citation: Advances in Difference Equations 2019 2019:303

    Content type: Research

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  17. Some similarity solutions of the time-fractional stationary transonic plane-parallel gas flows (STPPGF) and their generalized space-fractional nonlinear system are obtained by using scalar similarity transform...

    Authors: Yufeng Zhang, Chao Yue and Xiangzhi Zhang

    Citation: Advances in Difference Equations 2019 2019:302

    Content type: Research

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  18. A leader-following consensus for Caputo fractional multi-agent systems with nonlinear intrinsic dynamics is investigated. The second Lyapunov method is used to design a control protocol ensuring a consensus fo...

    Authors: Ricardo Almeida, Ewa Girejko, Snezhana Hristova and Agnieszka B. Malinowska

    Citation: Advances in Difference Equations 2019 2019:301

    Content type: Research

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  19. This paper considers a non-autonomous modified Leslie–Gower model with Holling type IV functional response and nonlinear prey harvesting. The permanence of the model is obtained, and sufficient conditions for ...

    Authors: Jie Song, Yonghui Xia, Yuzhen Bai, Yaoxiong Cai and D. O’Regan

    Citation: Advances in Difference Equations 2019 2019:299

    Content type: Research

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  20. By using a solvability method for differential equations, we present an elegant and straightforward/direct proof of the following slight generalization of a classical result: Let ...

    Authors: Stevo Stević

    Citation: Advances in Difference Equations 2019 2019:298

    Content type: Research

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  21. In this study the method which was obtained from a combination of the conformable fractional double Laplace transform method and the Adomian decomposition method has been successfully applied to solve linear a...

    Authors: Hassan Eltayeb, Imed Bachar and Musa Gad-Allah

    Citation: Advances in Difference Equations 2019 2019:293

    Content type: Research

    Published on:

  22. We investigate the existence of solutions for new boundary value problems of Caputo-type sequential fractional differential equations and inclusions supplemented with nonlocal integro-multipoint boundary condi...

    Authors: Bashir Ahmad, Ahmed Alsaedi, Sotiris K. Ntouyas and Wafa Shammakh

    Citation: Advances in Difference Equations 2019 2019:290

    Content type: Research

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  23. In this article, we present a method to approximate the solution of a fractional Ricatti equation based on the ABFD in the Caputo sense. The proposed method depends on the fractional operational matrix of the ...

    Authors: M. Motawi Khashan and Muhammed I. Syam

    Citation: Advances in Difference Equations 2019 2019:288

    Content type: Research

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  24. Recent research has gained more attention on conformable integrals and derivatives to derive the various type of inequalities. One of the recent advancements in the field of fractional calculus is the generali...

    Authors: Gauhar Rahman, Aftab Khan, Thabet Abdeljawad and Kottakkaran Sooppy Nisar

    Citation: Advances in Difference Equations 2019 2019:287

    Content type: Research

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  25. We deal with a class of coupled systems of neutral fractional integro-differential equations with infinite delay in a Banach space in this paper. Based on the Banach contraction principle and Krasnoselskii’s f...

    Authors: Juqing Liu and Kaihong Zhao

    Citation: Advances in Difference Equations 2019 2019:284

    Content type: Research

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  26. In this paper, we propose and analyze a mathematical model of mealybugs and green lacewings with time delay to investigate the population dynamics of mealybugs (a major insect pest of cassava) and green lacewi...

    Authors: Kittipol Jankaew, Chontita Rattanakul and Warunee Sarika

    Citation: Advances in Difference Equations 2019 2019:283

    Content type: Research

    Published on:

  27. In this paper, the distributions of generalized zeros of oscillatory solutions for second-order nonlinear neutral delay difference equations are studied. By means of inequality techniques, specific function se...

    Authors: Limei Feng and Zhenlai Han

    Citation: Advances in Difference Equations 2019 2019:282

    Content type: Research

    Published on:

  28. In this paper, a non-selective harvesting Lotka–Volterra amensalism discrete model incorporating partial closure for the populations is proposed and studied. By applying the relevant conclusions of difference ...

    Authors: Qianqian Su and Fengde Chen

    Citation: Advances in Difference Equations 2019 2019:281

    Content type: Research

    Published on:

  29. In this paper, we study existence and nonexistence of positive solutions for a class of Riemann–Stieltjes integral boundary value problems of fractional differential equations with parameters. By using the fix...

    Authors: Mei Jia, Lin Li, Xiping Liu, Junqiu Song and Zhanbing Bai

    Citation: Advances in Difference Equations 2019 2019:280

    Content type: Research

    Published on:

  30. Considering the influence of the preferential degree, the hesitation psychology of customers and the heterogeneity of underlying networks in preferential information spreading, we propose a novel model called AHF...

    Authors: Xiongding Liu, Tao Li, Xinming Cheng, Wenjin Liu and Hao Xu

    Citation: Advances in Difference Equations 2019 2019:279

    Content type: Research

    Published on:

  31. The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo–Fabrizio fractional operator for the inclus...

    Authors: Devendra Kumar, Jagdev Singh, Maysaa Al Qurashi and Dumitru Baleanu

    Citation: Advances in Difference Equations 2019 2019:278

    Content type: Research

    Published on:

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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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