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  1. A new auxiliary result based on a three step quadratic kernel utilizing the concepts of local fractional calculus is obtained. Using this new auxiliary result we have several new Newton type inequalities whose...

    Authors: Sabah Iftikhar, Samet Erden, Poom Kumam and Muhammad Uzair Awan

    Citation: Advances in Difference Equations 2020 2020:185

    Content type: Research

    Published on:

  2. In this paper, we study the rubella disease model with the Caputo–Fabrizio fractional derivative. The mathematical solution of the liver model is presented by a three-step Adams–Bashforth scheme. The existence...

    Authors: Dumitru Baleanu, Hakimeh Mohammadi and Shahram Rezapour

    Citation: Advances in Difference Equations 2020 2020:184

    Content type: Research

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  3. The Editors-in-Chief have retracted this article [1] because it overlaps with articles by other authors that were simultaneously under consideration at different journals [2,3].

    Authors: Mingzhu Lai, Jianguo Sun and Wei Li

    Citation: Advances in Difference Equations 2020 2020:181

    Content type: Retraction Note

    Published on:

    The original article was published in Advances in Difference Equations 2017 2017:87

  4. A system of linear Riemann–Liouville fractional differential equations with constant delay is studied. The initial condition is set up similar to the case of the ordinary derivative. Explicit formulas for the ...

    Authors: S. Hristova, Ravi Agarwal and D. O’Regan

    Citation: Advances in Difference Equations 2020 2020:180

    Content type: Research

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  5. In this paper, we use an Ornstein–Uhlenbeck process to describe the environmental stochasticity and propose a stochastic predator–prey model with modified Leslie–Gower and Holling-type II schemes. For each spe...

    Authors: Dengxia Zhou, Meng Liu and Zhijun Liu

    Citation: Advances in Difference Equations 2020 2020:179

    Content type: Research

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  6. The primary purpose of this study is to perform the comparison of deterministic and stochastic modeling. The effect of threshold number is also observed in this model. For numerical simulations, we have develo...

    Authors: Ali Raza, Muhammad Rafiq, Dumitru Baleanu and Muhammad Shoaib Arif

    Citation: Advances in Difference Equations 2020 2020:176

    Content type: Research

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  7. This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the...

    Authors: Abdul Majeed, Mohsin Kamran, Muhammad Kashif Iqbal and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:175

    Content type: Research

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  8. A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed ...

    Authors: P. Veeresha, D. G. Prakasha, Jagdev Singh, Ilyas Khan and Devendra Kumar

    Citation: Advances in Difference Equations 2020 2020:174

    Content type: Research

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  9. In this paper, we propose an efficient B-spline finite element method for a class of fourth order nonlinear differential equations with variable coefficient. For the temporal discretization, we choose the Cran...

    Authors: Dandan Qin, John Jiawei Tan, Bo Liu and Wenzhu Huang

    Citation: Advances in Difference Equations 2020 2020:172

    Content type: Research

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  10. In this paper, our main purpose is to present an analytical solution for measles spread model with three doses of vaccination using Caputo–Fabrizio fractional derivative (CFFD). The presented solution is based...

    Authors: Ghazala Nazir, Kamal Shah, Hussam Alrabaiah, Hammad Khalil and Rahmat Ali Khan

    Citation: Advances in Difference Equations 2020 2020:171

    Content type: Research

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  11. The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of ...

    Authors: Taekyun Kim, Dae San Kim, Jongkyum Kwon and Hyunseok Lee

    Citation: Advances in Difference Equations 2020 2020:168

    Content type: Research

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  12. This work mainly investigates the separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio fractional derivatives. An inequality ensuring the positivity of the fractional derivative...

    Authors: Wenyong Zhong, Lanfang Wang and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2020 2020:166

    Content type: Research

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  13. In this paper, we investigate the existence of solutions for two nonlinear fractional multi-term integro-differential inclusions in two hybrid and non-hybrid versions. The boundary value conditions are in the ...

    Authors: Sina Etemad, Shahram Rezapour and Mohammad Esmael Samei

    Citation: Advances in Difference Equations 2020 2020:161

    Content type: Research

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  14. The objective in this work is to study oscillation criteria for second-order quasi-linear differential equations with an advanced argument. We establish new oscillation criteria using both the comparison techn...

    Authors: G. E. Chatzarakis, O. Moaaz, T. Li and B. Qaraad

    Citation: Advances in Difference Equations 2020 2020:160

    Content type: Research

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  15. We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate solution of time fractional Allen–Cahn equation (ACE). We discret...

    Authors: Nauman Khalid, Muhammad Abbas, Muhammad Kashif Iqbal and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:158

    Content type: Research

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  16. In this paper, we investigate the existence of mild solutions for neutral Hilfer fractional evolution equations with noninstantaneous impulsive conditions in a Banach space. We obtain the existence results by ...

    Authors: Pallavi Bedi, Anoop Kumar, Thabet Abdeljawad and Aziz Khan

    Citation: Advances in Difference Equations 2020 2020:155

    Content type: Research

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  17. In this article, new definitions of fractional substantial sum and difference operators are introduced. Some properties are established and used to generate a fixed point operator for an arbitrary real order s...

    Authors: Syed Sabyel Haider and Mujeeb ur Rehman

    Citation: Advances in Difference Equations 2020 2020:154

    Content type: Research

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  18. This paper discusses the functional scattered data interpolation to interpolate the general scattered data. Compared with the previous works, we construct a new cubic Bézier-like triangular basis function cont...

    Authors: Samsul Ariffin Abdul Karim, Azizan Saaban, Vaclav Skala, Abdul Ghaffar, Kottakkaran Sooppy Nisar and Dumitru Baleanu

    Citation: Advances in Difference Equations 2020 2020:151

    Content type: Research

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  19. In this paper, we investigate hybrid adaptive synchronization issue for a class of perturbed fractional-order chaotic systems with nondeterministic nonlinear terms. On the basis of fractional-order extended ve...

    Authors: Funing Lin, Guangming Xue, Guangwang Su and Bin Qin

    Citation: Advances in Difference Equations 2020 2020:150

    Content type: Research

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  20. This article aims to establish certain image formulas associated with the fractional calculus operators with Appell function in the kernel and Caputo-type fractional differential operators involving Srivastava...

    Authors: Kottakkaran Sooppy Nisar, D. L. Suthar, R. Agarwal and S. D. Purohit

    Citation: Advances in Difference Equations 2020 2020:148

    Content type: Research

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  21. Dengue fever is a common disease which can cause shock, internal bleeding, and death in patients if a second infection is involved. In this paper, a multi-serotype dengue model with nonlinear incidence rate is...

    Authors: Sutawas Janreung, Wirawan Chinviriyasit and Settapat Chinviriyasit

    Citation: Advances in Difference Equations 2020 2020:147

    Content type: Research

    Published on:

  22. The Editors-in-Chief have retracted this article [1] because it significantly overlaps with an article by different authors [2] that was simultaneously under consideration at a different journal. The article a...

    Authors: Jianjie Wang, Jun Pu and Ahmed Zama

    Citation: Advances in Difference Equations 2020 2020:145

    Content type: Retraction Note

    Published on:

    The original article was published in Advances in Difference Equations 2016 2016:33

  23. A synthetic drug transmission model with psychological addicts and time delay is proposed in this paper. By analyzing the corresponding characteristic equation and choosing the time delay as the bifurcation pa...

    Authors: Zizhen Zhang, Fangfang Yang and Wanjun Xia

    Citation: Advances in Difference Equations 2020 2020:144

    Content type: Research

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  24. In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispe...

    Authors: Hui Zhou, Jehad Alzabut, Shahram Rezapour and Mohammad Esmael Samei

    Citation: Advances in Difference Equations 2020 2020:143

    Content type: Research

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  25. In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained res...

    Authors: Dafang Zhao, Muhammad Aamir Ali, Artion Kashuri and Hüseyin Budak

    Citation: Advances in Difference Equations 2020 2020:137

    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