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Theory and Modern Applications

Advances in Continuous and Discrete Models Cover Image

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  1. In the present paper, we consider a fractional discrete Schrödinger equation with Kirchhoff term. Through the fountain theorem and the dual fountain theorem, we obtain two different conclusions about infinitel...

    Authors: Chunming Ju, Giovanni Molica Bisci and Binlin Zhang
    Citation: Advances in Continuous and Discrete Models 2023 2023:31
  2. Self-similar finite-time singularity solutions of the axisymmetric Euler equations in an infinite system with a swirl are provided. Using the Elgindi approximation of the Biot–Savart kernel for the velocity in...

    Authors: Rodrigo Cádiz, Diego Martínez-Argüello and Sergio Rica
    Citation: Advances in Continuous and Discrete Models 2023 2023:30
  3. In this paper, a model of branching processes with random control functions and affected by viral infectivity in independent and identically distributed random environments is established, and the Markov prope...

    Authors: Min Ren and Guanghui Zhang
    Citation: Advances in Continuous and Discrete Models 2023 2023:26
  4. This paper investigates the existence of positive periodic solutions for a periodic predator-prey model with fear effect and general functional responses. The general functional responses can cover the Holling...

    Authors: Ke Guo and Wanbiao Ma
    Citation: Advances in Continuous and Discrete Models 2023 2023:22
  5. Motivated by several applications, we investigate the well-posedness of a switched system composed by a system of linear hyperbolic balance laws and by a system of linear algebraic differential equations. This...

    Authors: Raul Borsche, Mauro Garavello and Damla Kocoglu
    Citation: Advances in Continuous and Discrete Models 2023 2023:19
  6. The aim of the current work is to generalize the well-known bisection method using quantum calculus approach. The results for different values of quantum parameter q are analyzed, and the rate of convergence for ...

    Authors: Ghazala Gulshan, Hüseyin Budak, Rashida Hussain and Asad Sadiq
    Citation: Advances in Continuous and Discrete Models 2023 2023:18
  7. We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyse...

    Authors: David Ruelle
    Citation: Advances in Continuous and Discrete Models 2023 2023:17
  8. Although I had not previously been aware of Jean Ginibre’s work on random matrices, beginning in 1978 I became an admirer of his many papers on nonlinear waves in collaboration with Giorgio Velo. Their papers ...

    Authors: Walter A. Strauss
    Citation: Advances in Continuous and Discrete Models 2023 2023:16
  9. In this paper, we propose a high-order nonlinear algorithm based on a finite difference method modification to the regularized long wave equation and the Benjamin–Bona–Mahony–Burgers equation subject to the ho...

    Authors: Kanyuta Poochinapan and Ben Wongsaijai
    Citation: Advances in Continuous and Discrete Models 2023 2023:13
  10. In this paper, we are concerned with the stabilization of hybrid stochastic systems with variable delay by discrete-time state feedback control. By using Lyapunov functionals, we obtain an upper bound

    Authors: Wei Mao, Xiao Xiao, Liangliang Miao and Liangjian Hu
    Citation: Advances in Continuous and Discrete Models 2023 2023:12
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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

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