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  1. This paper will solve one of the fractional mathematical physics models, a one-dimensional time-fractional differential equation, by utilizing the second-order quarter-sweep finite-difference scheme and the pr...

    Authors: Andang Sunarto, Praveen Agarwal, Jumat Sulaiman, Jackel Vui Lung Chew and Elayaraja Aruchunan

    Citation: Advances in Difference Equations 2021 2021:147

    Content type: Research

    Published on:

  2. In this paper, a general class of Clifford-valued neutral high-order neural network (HNN) with D-operator on time scales is investigated. In this model, time-varying delays and continuously distributed delays are...

    Authors: Chaouki Aouiti, Imen Ben Gharbia, Jinde Cao and Xiaodi Li

    Citation: Advances in Difference Equations 2021 2021:145

    Content type: Research

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  3. In this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional ty...

    Authors: Muhammad Bahar Ali Khan, Thabet Abdeljawad, Kamal Shah, Gohar Ali, Hasib Khan and Aziz Khan

    Citation: Advances in Difference Equations 2021 2021:143

    Content type: Research

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  4. The Hirota bilinear method is employed for searching the localized waves, lump–solitons, and solutions between lumps and rogue waves for the fractional generalized Calogero–Bogoyavlensky–Schiff–Bogoyavlensky–K...

    Authors: Jalil Manafian, Onur Alp Ilhan, Ladan Avazpour and As’ad Alizadeh

    Citation: Advances in Difference Equations 2021 2021:141

    Content type: Research

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  5. To investigate the influences of heterogeneity and waning immunity on measles transmission, we formulate a network model with periodic transmission rate, and theoretically examine the threshold dynamics. We nu...

    Authors: Yuyi Xue, Xiaoe Ruan and Yanni Xiao

    Citation: Advances in Difference Equations 2021 2021:138

    Content type: Research

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  6. We investigate the existence of solutions for a nonlinear integral inclusion of Urysohn–Stieltjes type. As applications, we give a Chandrasekhar quadratic integral equation and a nonlinear Chandrasekhar integr...

    Authors: Ahmed El-Sayed, Shorouk Al-Issa and Yasmin Omar

    Citation: Advances in Difference Equations 2021 2021:137

    Content type: Research

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  7. In this paper, we investigate the analysis of the proportional Caputo derivative that recently has been constructed. We create some useful relations between this new derivative and beta function. We discretize...

    Authors: Ali Akgül and Dumitru Baleanu

    Citation: Advances in Difference Equations 2021 2021:136

    Content type: Research

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  8. Our basic purpose is to derive several existence aspects of solutions for a novel class of the fractional inclusion problem in terms of the well-defined generalized φ-Caputo and φ-Riemann–Liouville operators. The...

    Authors: Jehad Alzabut, Bashir Ahmad, Sina Etemad, Shahram Rezapour and Akbar Zada

    Citation: Advances in Difference Equations 2021 2021:135

    Content type: Research

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  9. A meta-model of diffusively coupled Lotka–Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of nth order solitary solut...

    Authors: Inga Timofejeva, Tadas Telksnys, Zenonas Navickas, Romas Marcinkevicius and Minvydas Ragulskis

    Citation: Advances in Difference Equations 2021 2021:133

    Content type: Research

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  10. Hand, foot, and mouth disease (HFMD) is a contagious viral illness that commonly affects infants and children. In some areas with high incidence of this disease, the relevant departments often use some strateg...

    Authors: Lei Shi, Hongyong Zhao and Daiyong Wu

    Citation: Advances in Difference Equations 2021 2021:130

    Content type: Research

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  11. The main aim presented in this article is to provide an efficient transferred Legendre pseudospectral method for solving pantograph delay differential equations. At the first step, we transform the problem int...

    Authors: H. Jafari, M. Mahmoudi and M. H. Noori Skandari

    Citation: Advances in Difference Equations 2021 2021:129

    Content type: Research

    Published on:

  12. In this paper, the authors present a strategy based on fixed point iterative methods to solve a nonlinear dynamical problem in a form of Green’s function with boundary value problems. First, the authors constr...

    Authors: Khanitin Muangchoo-in, Kanokwan Sitthithakerngkiet, Parinya Sa-Ngiamsunthorn and Poom Kumam

    Citation: Advances in Difference Equations 2021 2021:128

    Content type: Research

    Published on:

  13. This paper deals with the finite time stability and control for a class of uncertain variable fractional order nonlinear systems. The variable fractional Lyapunov direct method is developed to provide the basi...

    Authors: Jingfei Jiang, Hongkui Li, Kun Zhao, Dengqing Cao and Juan L. G. Guirao

    Citation: Advances in Difference Equations 2021 2021:127

    Content type: Research

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  14. The fractional Hopfield neural network (HNN) model is studied here analyzing its symmetry, uniqueness of the solution, dissipativity, fixed points etc. A Lyapunov and bifurcation analysis of the system is done...

    Authors: Emad E. Mahmoud, Lone Seth Jahanzaib, Pushali Trikha and Omar A. Almaghrabi

    Citation: Advances in Difference Equations 2021 2021:126

    Content type: Research

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  15. 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

    Content type: Research

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  16. 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

    Content type: Research

    Published on:

  17. 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

    Content type: Research

    Published on:

  18. 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

    Content type: Review

    Published on:

  19. 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

    Content type: Research

    Published on:

  20. 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

    Content type: Research

    Published on:

  21. 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

    Content type: Retraction Note

    Published on:

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

  22. 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

    Content type: Research

    Published on:

  23. 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

    Content type: Research

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  24. 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

    Content type: Research

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  25. 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

    Content type: Research

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  26. 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

    Content type: Research

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  27. 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

    Content type: Research

    Published on:

  28. 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

    Content type: Research

    Published on:

  29. 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

    Content type: Research

    Published on:

  30. 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

    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