Advances in Continuous and Discrete Models

Journal Article

Dynamical analysis of a novel fractional order SIDARTHE epidemic model of COVID-19 with the Caputo–Fabrizio(CF) derivative

Zhao, Yu; Li, Tian-zeng; Kang, Rong; He, Xi-liang

2024 Advances in Continuous and Discrete Models

doi:10.1186/s13662-024-03798-4

Fabrizio and Caputo suggested an extraordinary definition of fractional derivative, which has been used in many fields. The SIDARTHE infectious disease model with regard to COVID-19 is studied by the new notion in this paper. Making use of the Banach fixed point theorem, the existence and...

Open Access

Journal Article

Random exponential attractor for a stochastic reaction-diffusion equation in L2p(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{2p}(D)$\end{document}

Wang, Gang; Hu, Chaozhu

2024 Advances in Continuous and Discrete Models

doi:10.1186/s13662-023-03795-z

In this paper, we establish some sufficient conditions for the existence of a random exponential attractor for a random dynamical system in a Banach space. As an application, we consider a stochastic reaction-diffusion equation with multiplicative noise. We show that the random dynamical system...

Open Access

Journal Article

Study on the stability and its simulation algorithm of a nonlinear impulsive ABC-fractional coupled system with a Laplacian operator via F-contractive mapping

Zhao, Kaihong

2024 Advances in Continuous and Discrete Models

doi:10.1186/s13662-024-03801-y

In this paper, we study the solvability and generalized Ulam–Hyers (UH) stability of a nonlinear Atangana–Baleanu–Caputo (ABC) fractional coupled system with a Laplacian operator and impulses. First, this system becomes a nonimpulsive system by applying an appropriate transformation. Secondly,...

Open Access

Journal Article

On the maximum principle for relaxed control problems of nonlinear stochastic systems

Mezerdi, Meriem; Mezerdi, Brahim

2024 Advances in Continuous and Discrete Models

doi:10.1186/s13662-024-03803-w

We consider optimal control problems for a system governed by a stochastic differential equation driven by a d-dimensional Brownian motion where both the drift and the diffusion coefficient are controlled. It is well known that without additional convexity conditions the strict control problem...

Open Access

Journal Article

Stability analysis of fractional order breast cancer model in chemotherapy patients with cardiotoxicity by applying LADM

Mohammadpoor, Hajar; Eghbali, Nasrin; Sajedi, Leila; Nosrati Sahlan, Monireh

2024 Advances in Continuous and Discrete Models

doi:10.1186/s13662-024-03800-z

Breast cancer is the most common type of cancer in women. Chemotherapy is primarily used for patients with stage 2 to 4 breast cancer. Most chemotherapy drugs are effective at destroying rapidly growing and proliferating cancer cells. However, drugs also damage normal, rapidly growing cells,...

Open Access

Journal Article

Controllability of stochastic fractional systems involving state-dependent delay and impulsive effects

Arthi, G.; Vaanmathi, M.; Ma, Yong-Ki

2024 Advances in Continuous and Discrete Models

doi:10.1186/s13662-024-03799-3

In this paper, the controllability concept of a nonlinear fractional stochastic system involving state-dependent delay and impulsive effects is addressed by employing Caputo derivatives and Mittag-Leffler (ML) functions. Based on stochastic analysis theory, novel sufficient conditions are derived...

Open Access

Journal Article

Casimir preserving stochastic Lie–Poisson integrators

Luesink, Erwin; Ephrati, Sagy; Cifani, Paolo; Geurts, Bernard

2024 Advances in Continuous and Discrete Models

doi:10.1186/s13662-023-03796-y

Casimir preserving integrators for stochastic Lie–Poisson equations with Stratonovich noise are developed, extending Runge–Kutta Munthe-Kaas methods. The underlying Lie–Poisson structure is preserved along stochastic trajectories. A related stochastic differential equation on the Lie algebra is...

Open Access

Journal Article

A mathematical model for evaluating the impact of nonpharmaceutical interventions on the early COVID-19 epidemic in the United Kingdom

Zhang, Hongyu; Jing, Shuanglin

2024 Advances in Continuous and Discrete Models

doi:10.1186/s13662-024-03802-x

The coronavirus disease 2019 (COVID-19) presents a severe and urgent threat to global health. In response to the COVID-19 pandemic, many countries have implemented nonpharmaceutical interventions (NPIs), including national workplace and school closures, personal protection, social distancing,...

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