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  1. In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward–backward splitting algorithm and the hybrid shrinking projection algorithm. We provide theoretica...

    Authors: Yasir Arfat, Poom Kumam, Muhammad Aqeel Ahmad Khan, Parinya Sa Ngiamsunthorn and Attapol Kaewkhao
    Citation: Advances in Difference Equations 2021 2021:124
  2. We first present a generalized class of binary interpolating refinement schemes and their properties. Then the refinement-schemes-based unified algorithms for the solution of certain nth order linear and nonlinea...

    Authors: Syeda Tehmina Ejaz, Ghulam Mustafa, Dumitru Baleanu and Yu-Ming Chu
    Citation: Advances in Difference Equations 2021 2021:121
  3. In this article, we introduce a class of stochastic matrix control functions to stabilize a nonlinear fractional Volterra integro-differential equation with Ψ-Hilfer fractional derivative. Next, using the fixed-p...

    Authors: Reza Chaharpashlou and Reza Saadati
    Citation: Advances in Difference Equations 2021 2021:118
  4. Fractional calculus was born in 1695 on September 30 due to a very deep question raised in a letter of L’Hospital to Leibniz. The prophetical answer of Leibniz to that deep question encapsulated a huge inspira...

    Authors: Dumitru Baleanu and Ravi P. Agarwal
    Citation: Advances in Difference Equations 2021 2021:117
  5. In this work, a sufficient condition required for the presence of positive solutions to a coupled system of fractional nonlinear differential equations of implicit type is studied. To study sufficient conditio...

    Authors: Muhammad Sarwar, Anwar Ali, Mian Bahadur Zada, Hijaz Ahmad and Taher A. Nofal
    Citation: Advances in Difference Equations 2021 2021:116
  6. The well-known novel virus (COVID-19) is a new strain of coronavirus family, declared by the World Health Organization (WHO) as a dangerous epidemic. More than 3.5 million positive cases and 250 thousand death...

    Authors: Mutaz Mohammad, Alexander Trounev and Carlo Cattani
    Citation: Advances in Difference Equations 2021 2021:115
  7. This article has been retracted. Please see the Retraction Notice for more detail: https://​doi.​org/​10.​1186/​s13662-021-03279-y

    Authors: Zain Ul Abadin Zafar, Kashif Rehan and M. Mushtaq
    Citation: Advances in Difference Equations 2021 2021:114

    The original article was published in Advances in Difference Equations 2017 2017:86

  8. In this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper “The within-host viral kinetics of SARS-CoV-2” published in (Math. Biosci. Eng. 17(4):2853–...

    Authors: Bhagya Jyoti Nath, Kaushik Dehingia, Vishnu Narayan Mishra, Yu-Ming Chu and Hemanta Kumar Sarmah
    Citation: Advances in Difference Equations 2021 2021:113
  9. In this paper we consider a standard class of the neural networks and propose an investigation of the global asymptotic stability of these neural systems. The main aim of this investigation is to define a nove...

    Authors: Yousef Gholami
    Citation: Advances in Difference Equations 2021 2021:112
  10. In this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods....

    Authors: Mohamed Abdelhakem, Doha Mahmoud, Dumitru Baleanu and Mamdouh El-kady
    Citation: Advances in Difference Equations 2021 2021:110
  11. In this paper, we construct a new Halpern-type subgradient extragradient iterative algorithm. The sequence generated by this algorithm converges strongly to a common solution of a variational inequality, an eq...

    Authors: Abdulmalik U. Bello and Monday O. Nnakwe
    Citation: Advances in Difference Equations 2021 2021:109
  12. In this article, we study a fractional order HIV/AIDS infection model with ABC-fractional derivative. The model is based on four classes of a population. The study includes the existence and uniqueness of solu...

    Authors: Muhammad Aslam, Rashid Murtaza, Thabet Abdeljawad, Ghaus ur Rahman, Aziz Khan, Hasib Khan and Haseena Gulzar
    Citation: Advances in Difference Equations 2021 2021:107
  13. COVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the CO...

    Authors: Mohammed A. Aba Oud, Aatif Ali, Hussam Alrabaiah, Saif Ullah, Muhammad Altaf Khan and Saeed Islam
    Citation: Advances in Difference Equations 2021 2021:106
  14. The aim of this research is to construct an SIR model for COVID-19 with fuzzy parameters. The SIR model is constructed by considering the factors of vaccination, treatment, obedience in implementing health pro...

    Authors: Muhammad Abdy, Syafruddin Side, Suwardi Annas, Wahyuddin Nur and Wahidah Sanusi
    Citation: Advances in Difference Equations 2021 2021:105
  15. In this paper, we establish some Hermite–Hadamard–Fejér type inclusions for the product of two co-ordinated convex interval-valued functions. These inclusions are generalizations of some results given in earli...

    Authors: Hasan Kara, Hüseyin Budak, Muhammad Aamir Ali, Mehmet Zeki Sarikaya and Yu-Ming Chu
    Citation: Advances in Difference Equations 2021 2021:104
  16. Applying the monotone iterative technique and the method of upper and lower solutions, we investigate the existence of extremal solutions for a nonlinear system of p-Laplacian differential equations with nonlocal...

    Authors: Bo Bi and Ying He
    Citation: Advances in Difference Equations 2021 2021:103
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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

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