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  1. This paper considers a one-dimensional thermoelastic Timoshenko beam system with suspenders, general weak internal damping with time varying coefficient, and time-varying delay terms. Under suitable conditions...

    Authors: Soh Edwin Mukiawa, Cyril Dennis Enyi and Salim A. Messaoudi
    Citation: Advances in Continuous and Discrete Models 2023 2023:7
  2. The goal of this article is to present a recently developed numerical approach for solving fractional stochastic differential equations with a singular Caputo kernel and a nonsingular Caputo–Fabrizio and Atang...

    Authors: Aisha F. Fareed, Menna T. M. Elbarawy and Mourad S. Semary
    Citation: Advances in Continuous and Discrete Models 2023 2023:5
  3. The history of the long-standing scientific collaboration between Jean Ginibre and Giorgio Velo is presented. The most important results obtained for a number of nonlinear dispersive partial differential equat...

    Authors: Giorgio Velo
    Citation: Advances in Continuous and Discrete Models 2023 2023:3
  4. It is widely accepted that financial data exhibit a long-memory property or a long-range dependence. In a continuous-time situation, the geometric fractional Brownian motion is an important model to characteri...

    Authors: Lin Sun, Jianxin Chen and Xianggang Lu
    Citation: Advances in Continuous and Discrete Models 2022 2022:69
  5. We analyze the initial-boundary value problem for the mixed nonlinear Schrödinger equation posed on the half-line by using the Fokas method. Assuming that a smooth solution exists, we show that the solution ca...

    Authors: Guenbo Hwang
    Citation: Advances in Continuous and Discrete Models 2022 2022:67
  6. The Rabinovich system can describe different physical interactions, including waves in plasmas, a convective fluid flow inside a rotating ellipsoid, and Kolmogorov’s flow interactions. This study considers the...

    Authors: Chernet Tuge Deressa
    Citation: Advances in Continuous and Discrete Models 2022 2022:66
  7. We prove the convergence of certain second-order numerical methods to weak solutions of the Navier–Stokes equations satisfying, in addition, the local energy inequality, and therefore suitable in the sense of ...

    Authors: Luigi C. Berselli and Stefano Spirito
    Citation: Advances in Continuous and Discrete Models 2022 2022:65
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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

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