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  1. By means of ς fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gron...

    Authors: Zareen A. Khan, Fahd Jarad, Aziz Khan and Hasib Khan

    Citation: Advances in Difference Equations 2021 2021:100

    Content type: Research

    Published on:

  2. Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynam...

    Authors: Salamida Daudi, Livingstone Luboobi, Moatlhodi Kgosimore, Dmitry Kuznetsov and Steady Mushayabasa

    Citation: Advances in Difference Equations 2021 2021:99

    Content type: Research

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  3. In this paper a model of Hopfield’s graded response neural network is investigated. A network whose neurons are subject to a certain impulsive state displacement at random times is considered. The model is set...

    Authors: R. Agarwal, S. Hristova, D. O’Regan and P. Kopanov

    Citation: Advances in Difference Equations 2021 2021:98

    Content type: Research

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  4. In this manuscript, some fixed point results for generalized contractive type mappings under mild conditions in the setting of double controlled metric spaces (in short, http://static-content.springer.com/image/art%3A10.1186%2Fs13662-021-03255-6/13662_2021_3255_Article_IEq1.gif ...

    Authors: Hasanen A. Hammad, Hassen Aydi and Nabil Mlaiki

    Citation: Advances in Difference Equations 2021 2021:97

    Content type: Research

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  5. We investigate the existence and uniqueness of solutions to a coupled system of the hybrid fractional integro-differential equations involving φ-Caputo fractional operators. To achieve this goal, we make use of a...

    Authors: Abdellatif Boutiara, Sina Etemad, Azhar Hussain and Shahram Rezapour

    Citation: Advances in Difference Equations 2021 2021:95

    Content type: Research

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  6. In this paper, we investigate a class of fractional-order gene regulatory networks with time-varying delays and structured uncertainties (UDFGRNs). First, we deduce the existence and uniqueness of the equilibr...

    Authors: Zhaohua Wu, Zhiming Wang and Tiejun Zhou

    Citation: Advances in Difference Equations 2021 2021:93

    Content type: Research

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  7. In this paper, a hybrid method called variational iteration transform method has been implemented to solve fractional-order Navier–Stokes equation. Caputo operator describes fractional-order derivatives. The s...

    Authors: Yu-Ming Chu, Nehad Ali Shah, Praveen Agarwal and Jae Dong Chung

    Citation: Advances in Difference Equations 2021 2021:91

    Content type: Research

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  8. Fractional calculus (FC) is useful in studying physical phenomena with memory effect. In this paper, a fractional form of Ambartsumian equation is considered utilizing the Caputo fractional derivative. The Hea...

    Authors: Abdelhalim Ebaid, Carlo Cattani, Amnah S. Al Juhani and Essam R. El-Zahar

    Citation: Advances in Difference Equations 2021 2021:88

    Content type: Research

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  9. Our aim in this article is to solve the composite fractional relaxation differential equation by using different definitions of the non-integer order derivative operator http://static-content.springer.com/image/art%3A10.1186%2Fs13662-021-03227-w/13662_2021_3227_Article_IEq1.gif ...

    Authors: Azhar Ali Zafar, Jan Awrejcewicz, Olga Mazur and Muhammad Bilal Riaz

    Citation: Advances in Difference Equations 2021 2021:87

    Content type: Research

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  10. In this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative ...

    Authors: Karim Khan, Rahat Zarin, Amir Khan, Abdullahi Yusuf, Mohammed Al-Shomrani and Arif Ullah

    Citation: Advances in Difference Equations 2021 2021:86

    Content type: Research

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  11. In this paper, we present a new sufficient condition for the oscillation of all solutions of linear delay differential equations. The obtained result improves known conditions in the literature. We also give a...

    Authors: George E. Chatzarakis, Božena Dorociaková and Rudolf Olach

    Citation: Advances in Difference Equations 2021 2021:85

    Content type: Research

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  12. The principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomia...

    Authors: Waleed M. Abd-Elhameed and Youssri H. Youssri

    Citation: Advances in Difference Equations 2021 2021:84

    Content type: Research

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  13. The definition of Stepanov-like almost automorphic functions on time scales had been proposed in the literature, but at least one result was incorrect, which involved Bochner transform. In our work, we give th...

    Authors: Li-Li Zhang and Xu-Dong Yang

    Citation: Advances in Difference Equations 2021 2021:83

    Content type: Research

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  14. Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized ...

    Authors: Dumitru Baleanu, Artion Kashuri, Pshtiwan Othman Mohammed and Badreddine Meftah

    Citation: Advances in Difference Equations 2021 2021:82

    Content type: Research

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  15. In this note, we broaden the utilization of an efficient computational scheme called the approximate analytical method to obtain the solutions of fractional-order Navier–Stokes model. The approximate analytica...

    Authors: Umar Farooq, Hassan Khan, Fairouz Tchier, Evren Hincal, Dumitru Baleanu and Haifa Bin Jebreen

    Citation: Advances in Difference Equations 2021 2021:81

    Content type: Research

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  16. Based on the effects of white noise and colored noise, we propose a stochastic Holling-III predator–prey model in an impulsive polluted environment. Firstly, we prove an existence and uniqueness theorem of the...

    Authors: Wen Qin, Hanjun Zhang and Qingsong He

    Citation: Advances in Difference Equations 2021 2021:80

    Content type: Research

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  17. For the high-dimensional Frenkel–Kontorova model on lattices, we have concluded that there are heteroclinic connections between neighboring Birkhoff minimizers which are more periodic. This conclusion is based...

    Authors: Xue-Qing Miao

    Citation: Advances in Difference Equations 2021 2021:79

    Content type: Research

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  18. In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory and by constructing a suitable Lyapun...

    Authors: Lihua Dai, Junjie Wang, Yonggen Ni and Bin Xu

    Citation: Advances in Difference Equations 2021 2021:76

    Content type: Research

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  19. In this paper, we mainly investigate upper semicontinuity and regularity of attractors for nonclassical diffusion equations with perturbed parameters ν and the nonlinear term f satisfying the polynomial growth of...

    Authors: Yongqin Xie, Jun Li and Kaixuan Zhu

    Citation: Advances in Difference Equations 2021 2021:75

    Content type: Research

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  20. This paper focuses on the stochastically exponential synchronization problem for one class of neural networks with time-varying delays (TDs) and Markov jump parameters (MJPs). To derive a tighter bound of reci...

    Authors: Xiaoman Liu, Haiyang Zhang, Jun Yang and Hao Chen

    Citation: Advances in Difference Equations 2021 2021:74

    Content type: Research

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  21. This paper studies a controlled backward-forward linear-quadratic-Gaussian (LQG) large population system in Stackelberg games. The leader agent is of backward state and follower agents are of forward state. The l...

    Authors: Kehan Si and Zhen Wu

    Citation: Advances in Difference Equations 2021 2021:73

    Content type: Research

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  22. Subdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and s...

    Authors: Mehwish Bari, Ghulam Mustafa, Abdul Ghaffar, Kottakkaran Sooppy Nisar and Dumitru Baleanu

    Citation: Advances in Difference Equations 2021 2021:72

    Content type: Research

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  23. In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order de...

    Authors: Erdal Karapinar, Ho Duy Binh, Nguyen Hoang Luc and Nguyen Huu Can

    Citation: Advances in Difference Equations 2021 2021:70

    Content type: Research

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  24. In the present paper, we find some characterization theorems. Under certain pinching conditions on the warping function satisfying some differential equation, we show that the base of warped product submanifol...

    Authors: Akram Ali, Ravi P. Agrawal, Fatemah Mofarreh and Nadia Alluhaibi

    Citation: Advances in Difference Equations 2021 2021:69

    Content type: Research

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  25. A newly proposed p-Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives. The existence and uniqueness of solutions are fully inve...

    Authors: M. M. Matar, M. I. Abbas, J. Alzabut, M. K. A. Kaabar, S. Etemad and S. Rezapour

    Citation: Advances in Difference Equations 2021 2021:68

    Content type: Research

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  26. In this paper, we obtain sufficient conditions for the existence and uniqueness results of the pantograph fractional differential equations (FDEs) with nonlocal conditions involving Atangana–Baleanu–Caputo (AB...

    Authors: Mohammed S. Abdo, Thabet Abdeljawad, Kishor D. Kucche, Manar A. Alqudah, Saeed M. Ali and Mdi Begum Jeelani

    Citation: Advances in Difference Equations 2021 2021:65

    Content type: Research

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  27. This research aims to discuss and control the chaotic behaviour of an autonomous fractional biological oscillator. Indeed, the concept of fractional calculus is used to include memory in the modelling formulat...

    Authors: Ali Saleh Alshomrani, Malik Zaka Ullah and Dumitru Baleanu

    Citation: Advances in Difference Equations 2021 2021:63

    Content type: Research

    Published on:

  28. In this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov ...

    Authors: Yumin Wu, Fengde Chen and Caifeng Du

    Citation: Advances in Difference Equations 2021 2021:62

    Content type: Research

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  29. In this work, a version of continuous stage stochastic Runge–Kutta (CSSRK) methods is developed for stochastic differential equations (SDEs). First, a general order theory of these methods is established by th...

    Authors: Xuan Xin, Wendi Qin and Xiaohua Ding

    Citation: Advances in Difference Equations 2021 2021:61

    Content type: Research

    Published on:

  30. In this study, we investigate reaction-diffusion complex-valued neural networks with mixed delays. The mixed delays include both time-varying and infinite distributed delays. Criteria are derived to ensure the...

    Authors: Xiaohui Xu, Jibin Yang, Quan Xu, Yanhai Xu and Shulei Sun

    Citation: Advances in Difference Equations 2021 2021:58

    Content type: Research

    Published on:

  31. Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented nu...

    Authors: Abdon Atangana and Seda İğret Araz

    Citation: Advances in Difference Equations 2021 2021:57

    Content type: Research

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  32. In this article, we first demonstrate a fixed point result under certain contraction in the setting of controlled b-Branciari metric type spaces.

    • Thereafter, we specifically co...

    Authors: Kalaivani Chandran, Kalpana Gopalan, Sumaiya Tasneem Zubair and Thabet Abdeljawad

    Citation: Advances in Difference Equations 2021 2021:56

    Content type: Research

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  33. In this paper, we study an initial value problem for a class of impulsive implicit-type fractional differential equations (FDEs) with proportional delay terms. Schaefer’s fixed point theorem and Banach’s contr...

    Authors: Arshad Ali, Ibrahim Mahariq, Kamal Shah, Thabet Abdeljawad and Bahaa Al-Sheikh

    Citation: Advances in Difference Equations 2021 2021:55

    Content type: Research

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  34. Dynamical analysis of a delayed tri-trophic food chain consisting of prey, an intermediate, and a top predator is investigated in this paper. The additive Allee effect is introduced in the prey population, and...

    Authors: S. Vinoth, R. Sivasamy, K. Sathiyanathan, Grienggrai Rajchakit, P. Hammachukiattikul, R. Vadivel and Nallappan Gunasekaran

    Citation: Advances in Difference Equations 2021 2021:54

    Content type: Research

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  35. In this paper, we study the oscillation of a class of third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales. By using Riccati transformation and integral inequality, we e...

    Authors: Zhiyu Zhang and Ruihua Feng

    Citation: Advances in Difference Equations 2021 2021:53

    Content type: Research

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  36. This paper is concerned with description of the existence and the forms of entire solutions of several second-order partial differential-difference equations with more general forms of Fermat type. By utilizin...

    Authors: Hong Yan Xu, Da Wei Meng, Sanyang Liu and Hua Wang

    Citation: Advances in Difference Equations 2021 2021:52

    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

Interim Editor-in-Chief

New Content ItemSong Wang, Curtin University, Australia | 

Song Wang's SpringerNature Publications