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  1. We revisit the persistence and stability property of a stage-structured prey–predator model with cannibalism and constant attacking rate. By using the differential inequality theory and Bendixson–Dulac criteri...

    Authors: Fengde Chen, Hang Deng, Zhenliang Zhu and Zhong Li

    Citation: Advances in Difference Equations 2020 2020:75

    Content type: Research

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  2. In this work we investigate existence and uniqueness of solutions for new coupled systems of mixed order fractional differential equations and inclusions supplemented with coupled nonlocal fractional boundary ...

    Authors: Sotiris K. Ntouyas and Hamed H. Al-Sulami

    Citation: Advances in Difference Equations 2020 2020:73

    Content type: Research

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  3. By using the fractional Caputo–Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fi...

    Authors: Dumitru Baleanu, Hakimeh Mohammadi and Shahram Rezapour

    Citation: Advances in Difference Equations 2020 2020:71

    Content type: Research

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  4. A stochastic susceptible–infectious–recovered epidemic model with temporary immunity and media coverage is proposed. The effects of Lévy jumps on the dynamics of the model are considered. A unique global posit...

    Authors: Yingfen Liu, Yan Zhang and Qingyun Wang

    Citation: Advances in Difference Equations 2020 2020:70

    Content type: Research

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  5. In this paper, the KdV-mKdV equation is obtained via the reductive perturbation method which can be applied to model the traffic flow. To overcome the shortcomings of the traditional KdV-mKdV equation, the ori...

    Authors: Cheng Li, Damin Cao and Qing Du

    Citation: Advances in Difference Equations 2020 2020:68

    Content type: Research

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  6. The objective of this paper is to investigate the approximate controllability of a semilinear impulsive stochastic system with nonlocal conditions and Poisson jumps in a Hilbert space. Nonlocal initial conditi...

    Authors: A. Anguraj, K. Ravikumar and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:65

    Content type: Research

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  7. This paper is concerned with a class of impulsive implicit fractional integrodifferential equations having the boundary value problem with mixed Riemann–Liouville fractional integral boundary conditions. We es...

    Authors: Akbar Zada, Jehad Alzabut, Hira Waheed and Ioan-Lucian Popa

    Citation: Advances in Difference Equations 2020 2020:64

    Content type: Research

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  8. This paper is concerned with a class of fractional neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion (fBm). First, by means of the resolvent operator techniqu...

    Authors: Jiankang Liu, Wei Xu and Qin Guo

    Citation: Advances in Difference Equations 2020 2020:63

    Content type: Research

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  9. Novel explicit wave solutions are constructed for the Kudryashov–Sinelshchikov (KS) equation through liquid–gas bubbles mix under the thermodynamic conditions. A new fractional definition (Atangana–Baleanu der...

    Authors: Chen Yue, Mostafa M. A. Khater, Raghda A. M. Attia and Dianchen Lu

    Citation: Advances in Difference Equations 2020 2020:62

    Content type: Research

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  10. In this article, we mainly develop a reduced order extrapolating model for the solution coefficient vectors of the classical collocation spectral (CCS) scheme to the two-dimensional (2D) telegraph equation by ...

    Authors: Hui Wang, Qingfang He and Zhendong Luo

    Citation: Advances in Difference Equations 2020 2020:61

    Content type: Research

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  11. This paper is concerned with the existence of continuous solutions of a set-valued functional integral equation of Volterra–Stieltjes type. The continuous dependence of the solution on the set of selections of...

    Authors: Ahmed Mohamed El-Sayed and Shorouk Mahmoud Al-Issa

    Citation: Advances in Difference Equations 2020 2020:59

    Content type: Research

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  12. In the present paper, by using the variational and topological methods, we obtain a multiplicity and bifurcation result for the following fractional problems involving critical nonlinearities and a lower order...

    Authors: Jiabin Zuo, Mingwei Li, Bomeng Li and Zhenhua Qiao

    Citation: Advances in Difference Equations 2020 2020:58

    Content type: Research

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  13. The Editors-in-Chief have retracted this article [1] because it shows significant overlap with an article by different authors that was simultaneously under consideration with another journal [2] and with a pr...

    Authors: Zhenhai Yan and Beatriz Ychussie

    Citation: Advances in Difference Equations 2020 2020:56

    Content type: Retraction Note

    Published on:

    The original article was published in Advances in Difference Equations 2015 2015:226

  14. In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fra...

    Authors: Shahram Alizadeh, Dumitru Baleanu and Shahram Rezapour

    Citation: Advances in Difference Equations 2020 2020:55

    Content type: Research

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  15. We approximate the solution of the nonlinear Fredholm integro-differential equation (NFID) in the complex plane by periodic quasi-wavelets (PQWs). This kind of wavelets possesses orthonormality properties, the...

    Authors: M. Erfanian, H. Zeidabadi and M. Parsamanesh

    Citation: Advances in Difference Equations 2020 2020:52

    Content type: Research

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  16. In this paper, a class of fractional boundary value problems with a parameter are discussed. We give some sufficient conditions to guarantee that above problems have a unique solution and construct the corresp...

    Authors: Yanbin Sang and Luxuan He

    Citation: Advances in Difference Equations 2020 2020:51

    Content type: Research

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  17. A fractional-order eco-epidemiological model with disease in the prey population is formulated and analyzed. Mathematical analysis and numerical simulations are performed to clarify the characteristics of the ...

    Authors: Mahmoud Moustafa, Mohd Hafiz Mohd, Ahmad Izani Ismail and Farah Aini Abdullah

    Citation: Advances in Difference Equations 2020 2020:48

    Content type: Research

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  18. In this paper, we are concerned with a class of quaternion-valued cellular neural networks with time-varying transmission delays and leakage delays. By applying a continuation theorem of coincidence degree the...

    Authors: Yongkun Li and Jianglian Xiang

    Citation: Advances in Difference Equations 2020 2020:47

    Content type: Research

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  19. In this paper, we broaden the utilization of a beautiful computational scheme, residual power series method (RPSM), to attain the fractional power series solutions of nonhomogeneous and homogeneous nonlinear t...

    Authors: Ved Prakash Dubey, Rajnesh Kumar, Devendra Kumar, Ilyas Khan and Jagdev Singh

    Citation: Advances in Difference Equations 2020 2020:46

    Content type: Research

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  20. We investigate the dynamical behavior of a modified Leslie–Gower prey–predator model with harvesting in prey population. In order to explore rich dynamics of the model, Euler approximation is implemented to ob...

    Authors: Muhammad Bilal Ajaz, Umer Saeed, Qamar Din, Irfan Ali and Muhammad Israr Siddiqui

    Citation: Advances in Difference Equations 2020 2020:45

    Content type: Research

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  21. This paper investigates a periodic Nicholson’s blowflies equation with multiple time-varying delays. By using differential inequality techniques and the fluctuation lemma, we establish a criterion to ensure th...

    Authors: Qian Cao, Guoqiu Wang and Chaofan Qian

    Citation: Advances in Difference Equations 2020 2020:43

    Content type: Research

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  22. It is important that we increase our ability for studying of complicate fractional integro-differential equation. In this paper, we investigates the existence of solutions for a pointwise defined multi-singula...

    Authors: Mandana Talaee, Mehdi Shabibi, Alireza Gilani and Shahram Rezapour

    Citation: Advances in Difference Equations 2020 2020:41

    Content type: Research

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  23. In the article, we present the explicit bounds for three generalized delay dynamic Gronwall–Bellman type integral inequalities on time scales, which are the unification of continuous and discrete results. As a...

    Authors: Sobia Rafeeq, Humaira Kalsoom, Sabir Hussain, Saima Rashid and Yu-Ming Chu

    Citation: Advances in Difference Equations 2020 2020:40

    Content type: Research

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  24. Fractional kinetic equations (FKEs) including a wide variety of special functions have been widely and successfully applied in describing and solving many important problems of physics and astrophysics. In thi...

    Authors: Kottakkaran Sooppy Nisar, Amjad Shaikh, Gauhar Rahman and Dinesh Kumar

    Citation: Advances in Difference Equations 2020 2020:39

    Content type: Research

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  25. This work deals with the bounds of a unified integral operator with which several fractional and conformable integral operators are directly associated. By using quasiconvex and monotone functions we establish...

    Authors: Dongming Zhao, Ghulam Farid, Muhammad Zeb, Sohail Ahmad and Kahkashan Mahreen

    Citation: Advances in Difference Equations 2020 2020:38

    Content type: Research

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  26. We consider distributed-order partial differential equations with time fractional derivative proposed by Caputo and Fabrizio in a one-dimensional space. Two finite difference schemes are established via Grünwa...

    Authors: Haili Qiao, Zhengguang Liu and Aijie Cheng

    Citation: Advances in Difference Equations 2020 2020:36

    Content type: Research

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  27. The spread of an epidemic diseases is stochastic in nature. It is more realistic to include this stochasticity when modelling the dynamics of a communicable disease. In this paper, a stochastic model for foot ...

    Authors: Kamaleldin Abodayeh, Muhammad Shoaib Arif, Ali Raza, Muhammad Rafiq, Mairaj Bibi and Amna Nazeer

    Citation: Advances in Difference Equations 2020 2020:34

    Content type: Research

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  28. In this paper, we study some new Volterra–Fredholm type dynamical integral inequalities in two independent variables on time scale pairs, which provide explicit bounds on unknown functions. These inequalities ...

    Authors: Haidong Liu and Chuancun Yin

    Citation: Advances in Difference Equations 2020 2020:31

    Content type: Research

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  29. This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction–diffusion equations (TFCRDEs)...

    Authors: Sunil Kumar, Amit Kumar, Syed Abbas, Maysaa Al Qurashi and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:28

    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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