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  1. Nonorthogonal polynomials have many useful properties like being used as a basis for spectral methods, being generated in an easy way, having exponential rates of convergence, having fewer terms and reducing c...

    Authors: Sh. Karami, A. Fakharzadeh Jahromi and M. H. Heydari
    Citation: Advances in Continuous and Discrete Models 2022 2022:64
  2. This paper investigates the quasiconsensus problem of fractional-order heterogeneous multiagent systems, the distributed impulsive control protocol is designed for the multiagent system. In contrast to some ex...

    Authors: Conggui Huang, Fei Wang and Zhaowen Zheng
    Citation: Advances in Continuous and Discrete Models 2022 2022:63
  3. This paper investigates a globally coupled map lattice. Rigorous proofs to the existence of chaos in the sense of both Li–Yorke and Devaney in two controlled globally coupled map lattices are presented. In add...

    Authors: Yadan Yu, Wei Liang and Taiyan Jing
    Citation: Advances in Continuous and Discrete Models 2022 2022:62
  4. Peridynamic (PD) theories have become widespread in various research areas due to the ability of modeling discontinuity formation and evolution in materials. Bond-based peridynamics (BB-PD), notwithstanding so...

    Authors: Nunzio Dimola, Alessandro Coclite, Giuseppe Fanizza and Tiziano Politi
    Citation: Advances in Continuous and Discrete Models 2022 2022:60
  5. We devise a numerical scheme for computing arc-length parameterized curves of low bending energy that are confined to convex domains. We address the convergence of the discrete formulations to a continuous mod...

    Authors: Sören Bartels and Pascal Weyer
    Citation: Advances in Continuous and Discrete Models 2022 2022:58
  6. In this work, the Chebyshev collocation scheme is extended for the Volterra integro-differential equations of pantograph type. First, we construct the operational matrices of pantograph and derivative based on...

    Authors: Tianfu Ji, Jianhua Hou and Changqing Yang
    Citation: Advances in Continuous and Discrete Models 2022 2022:57
  7. Image denoising approaches based on partial differential modeling have attracted a lot of attention in image processing due to their high performance. The nonlinear anisotropic diffusion equations, specially P...

    Authors: Jalil Mazloum and Behrang Hadian Siahkal-Mahalle
    Citation: Advances in Continuous and Discrete Models 2022 2022:56
  8. In this paper, we focus on the development and study of the finite difference/pseudo-spectral method to obtain an approximate solution for the time-fractional diffusion-wave equation in a reproducing kernel Hi...

    Authors: Mojtaba Fardi, Shrideh K. Qasem Al-Omari and Serkan Araci
    Citation: Advances in Continuous and Discrete Models 2022 2022:54
  9. In this paper, we construct a new linear second-order finite difference scheme with two parameters for space-fractional Allen–Cahn equations. We first prove that the discrete maximum principle holds under reas...

    Authors: Kai Wang, Jundong Feng, Hongbo Chen and Changling Xu
    Citation: Advances in Continuous and Discrete Models 2022 2022:53
  10. The goal of this paper is to present a new class of operators satisfying the Prešić-type rational η-contraction condition in the setting of usual metric spaces. New fixed point results are also obtained for these...

    Authors: Hasanen A. Hammad, Mohamed Elmursi, Rashwan A. Rashwan and Hüseyin Işık
    Citation: Advances in Continuous and Discrete Models 2022 2022:52
  11. This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional deriva...

    Authors: Zakieh Avazzadeh, Omid Nikan, José Tenreiro Machado and Mohammad Navaz Rasoulizadeh
    Citation: Advances in Continuous and Discrete Models 2022 2022:48
  12. We examine a class of nonlinear fractional Mathieu equations with a damping term. The equation is an important equation of mathematical physics as it has many applications in various fields of the physical sci...

    Authors: Amel Berhail, Nora Tabouche, Jehad Alzabut and Mohammad Esmael Samei
    Citation: Advances in Continuous and Discrete Models 2022 2022:44
  13. In this manuscript, we examine both the existence and the stability of solutions to the boundary value problem of Caputo fractional differential equations of variable order by converting it into an equivalent ...

    Authors: Amar Benkerrouche, Mohammed Said Souid, Fahd Jarad and Ali Hakem
    Citation: Advances in Continuous and Discrete Models 2022 2022:43
  14. The uncertain production-inventory problem with deteriorating items is investigated and an optimal control model is developed in the present paper. The uncertain production-inventory problem is perturbed by an...

    Authors: Jiayu Shen, Yueqiang Jin, Bing Liu, Ziqiang Lu and Xin Chen
    Citation: Advances in Continuous and Discrete Models 2022 2022:42
  15. In this article, we present a fractional Kersten–Krasil’shchik coupled KdV-mKdV nonlinear model associated with newly introduced Atangana–Baleanu derivative of fractional order which uses Mittag-Leffler functi...

    Authors: Naveed Iqbal, Thongchai Botmart, Wael W. Mohammed and Akbar Ali
    Citation: Advances in Continuous and Discrete Models 2022 2022:37
  16. In this paper, we investigate periodic boundary value problems for Caputo type fractional semilinear nonautonomous differential equations with non-instantaneous impulses. By using semigroup theory combined wit...

    Authors: Xue Wang and Bo Zhu
    Citation: Advances in Continuous and Discrete Models 2022 2022:36
  17. We investigate the fractional dynamics of a coronavirus mathematical model under a Caputo derivative. The Laplace–Adomian decomposition and Homotopy perturbation techniques are applied to attain the approximat...

    Authors: Adnan, Amir Ali, Mati ur Rahmamn, Zahir Shah and Poom Kumam
    Citation: Advances in Continuous and Discrete Models 2022 2022:34
  18. Nonlinear fractional difference equations are studied deeply and extensively by many scientists by using fixed-point theorems on different types of function spaces. In this study, we combine fixed-point theory...

    Authors: Pshtiwan Othman Mohammed, Hari Mohan Srivastava, Juan L. G. Guirao and Y. S. Hamed
    Citation: Advances in Continuous and Discrete Models 2022 2022:32
  19. Study of ecosystems has always been an interesting topic in the view of real-world dynamics. In this paper, we propose a fractional-order nonlinear mathematical model to describe the prelude of deteriorating q...

    Authors: Pushpendra Kumar, V. Govindaraj, Vedat Suat Erturk and Mohamed S. Mohamed
    Citation: Advances in Continuous and Discrete Models 2022 2022:31
  20. This paper studies the compression of partial differential operators using neural networks. We consider a family of operators, parameterized by a potentially high-dimensional space of coefficients that may var...

    Authors: Fabian Kröpfl, Roland Maier and Daniel Peterseim
    Citation: Advances in Continuous and Discrete Models 2022 2022:29
  21. This research paper designs the noninteger order SEITR dynamical model in the Caputo sense for tuberculosis. The authors of the article have classified the infection compartment into four different compartment...

    Authors: Jitendra Panchal, Falguni Acharya and Kanan Joshi
    Citation: Advances in Continuous and Discrete Models 2022 2022:27
  22. Fractional differential equations have recently demonstrated their importance in a variety of fields, including medicine, applied sciences, and engineering. The main objective of this study is to propose an Ad...

    Authors: Nur Amirah Zabidi, Zanariah Abdul Majid, Adem Kilicman and Zarina Bibi Ibrahim
    Citation: Advances in Continuous and Discrete Models 2022 2022:26
  23. In this paper, we introduce and study a new accelerated algorithm based on forward–backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous function...

    Authors: Pornsak Yatakoat, Suthep Suantai and Adisak Hanjing
    Citation: Advances in Continuous and Discrete Models 2022 2022:25
  24. In this paper, we establish some new inequalities of Simpson’s type for differentiable convex functions involving some parameters and generalized fractional integrals. The results given in this study are a gen...

    Authors: Xuexiao You, Muhammad Aamir Ali, Hüseyin Budak, Hasan Kara and Dafang Zhao
    Citation: Advances in Continuous and Discrete Models 2022 2022:22
  25. This work is concerned with the issue of dissipative filtering for stochastic semi-Markovian jump via neural networks where the time-varying delay is based upon another semi-Markov process. Dissipative perform...

    Authors: Muhammad Shamrooz Aslam, Qianmu Li, Jun Hou and Hua Qiulong
    Citation: Advances in Continuous and Discrete Models 2022 2022:21
  26. We consider a version of the pole placement problem for tempered one-sided linear discrete-time time-varying linear systems. We prove a sufficient condition for assignability of the nonuniform dichotomy spectr...

    Authors: Artur Babiarz, Adam Czornik and Stefan Siegmund
    Citation: Advances in Continuous and Discrete Models 2022 2022:20
  27. In this paper, we investigate the partial asymptotic stability (PAS) of neutral pantograph stochastic differential equations with Markovian switching (NPSDEwMSs). The main tools used to show the results are th...

    Authors: Lassaad Mchiri, Tomás Caraballo and Mohamed Rhaima
    Citation: Advances in Continuous and Discrete Models 2022 2022:18
  28. According to the theory of regular geometric functions, the relevance of geometry to analysis is a critical feature. One of the significant tools to study operators is to utilize the convolution product. The d...

    Authors: F. Ghanim, Hiba F. Al-Janaby and Omar Bazighifan
    Citation: Advances in Continuous and Discrete Models 2022 2022:17
  29. The objective of this article is to study a three-step iteration process in the framework of Banach spaces and to obtain convergence results for Suzuki generalized nonexpansive mappings. We also provide numeri...

    Authors: Izhar Uddin, Chanchal Garodia, Thabet Abdeljawad and Nabil Mlaiki
    Citation: Advances in Continuous and Discrete Models 2022 2022:16
  30. In this paper, the dynamical behavior of a mathematical model of cancer including tumor cells, immune cells, and normal cells is investigated when a delay term is induced. Though the model was originally propo...

    Authors: Anusmita Das, Kaushik Dehingia, Hemanta Kumar Sarmah, Kamyar Hosseini, Khadijeh Sadri and Soheil Salahshour
    Citation: Advances in Continuous and Discrete Models 2022 2022:15

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