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  1. In this article, we introduce the concept of orthogonal m-metric space and prove some fixed point theorems in this space. Furthermore, we obtain results that extend and improve certain comparable results in the e...

    Authors: Fahim Uddin, Choonkil Park, Khalil Javed, Muhammad Arshad and Jung Rye Lee

    Citation: Advances in Difference Equations 2021 2021:159

    Content type: Research

    Published on:

  2. We investigate a model of spatio-temporal spreading of human immunodeficiency virus HIV-1. The mathematical model considers the presence of various components in a human tissue, including the uninfected CD4+T cel...

    Authors: Joel Alba-Pérez and Jorge E. Macías-Díaz

    Citation: Advances in Difference Equations 2021 2021:158

    Content type: Research

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  3. In this paper, the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system are investigated. We mainly analyze, control, and synchronize the associated hyperchaot...

    Authors: Dumitru Baleanu, Samaneh Sadat Sajjadi, Jihad H. Asad, Amin Jajarmi and Elham Estiri

    Citation: Advances in Difference Equations 2021 2021:157

    Content type: Research

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  4. In this article, first, we present an example of fuzzy normed space by means of the Mittag-Leffler function. Next, we extend the concept of fuzzy normed space to matrix valued fuzzy normed space and also we in...

    Authors: Safoura Rezaei Aderyani and Reza Saadati

    Citation: Advances in Difference Equations 2021 2021:154

    Content type: Research

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  5. This paper investigates singularly perturbed parabolic partial differential equations with delay in space, and the right end plane is an integral boundary condition on a rectangular domain. A small parameter i...

    Authors: Sekar Elango, Ayyadurai Tamilselvan, R. Vadivel, Nallappan Gunasekaran, Haitao Zhu, Jinde Cao and Xiaodi Li

    Citation: Advances in Difference Equations 2021 2021:151

    Content type: Research

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  6. 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

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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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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  16. 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:

  17. 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

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  18. 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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  19. 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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  20. 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

    Published on:

  21. 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

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  22. 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:

  23. 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:

  24. 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:

  25. 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:

  26. 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

  27. 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:

  28. 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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  29. 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

    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

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