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An editorial focuses on the recent advancements in fractional calculus and its applications in physical systems. It emphasizes the utility of fractional calculus in describing complex systems with nonlocal characteristics. The versatility of fractional calculus across various scientific disciplines, including physics, engineering, and biology, is highlighted.

The purpose of the present research is to improve our understanding of how coronavirus infection spreads by creating an epidemic model that incorporates isolation and quarantine measures. The dynamics of this viral spread are represented using the Caputo–Fabrizio operator. By analyzing the equilibria of the model and utilizing the next-generation matrix method, we determine the endemic indicator, R0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {R}}_0$$\end{document}. The main findings demonstrate that the equilibrium without infection is locally stable when R0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {R}}_0$$\end{document} is less than one and unstable otherwise. Also, we demonstrate the existence and uniqueness of the solution of our recommended model. In addition to this, we interrogate the solution pathways of the system by varying different factors, aiming to comprehend the intricate transmission of COVID-19 and visualize the crucial factors of the system that can aid public health officials in the control of the spread of infection. [ABSTRACT FROM AUTHOR]

The article presents the correction for a article titled "Recent advancement of fractional calculus and its applications in physical systems" published online on December 8, 2023.

It is evident that a tumor is a dangerous lump of tissue developed through the uncontrollable division of cells, replacing healthy tissue with abnormal tissue. It is cancerous and spreads through the lymphatic system or blood within the body of a host individual while the human immune system, consisting of interrelated special cells, tissues, and organs, is employed for the protection of the body from microorganisms, foreign diseases, infections, and toxins. Thus, the conceptualization and understanding of the intersections of tumor–immune cells are valuable. In this article, the natural process of tumor–immune cell interactions is formulated through a mathematical framework. The intricate dynamics of tumor–immune interactions are then represented by means of operators of fractional calculus involving nonlocal and nonsingular kernels. The definitions and basic properties of non-integer derivatives are introduced for the investigation of the proposed system. In addition, a new numerical scheme is introduced for the dynamics, showing the chaos and oscillation of the tumor–immune system. The proposed dynamics of tumor–immune interaction are highlighted with the effect of different input factors. Our findings not only contribute to a thorough comprehension of the complex interactions between input parameters and tumor dynamics, but critical factors that have a major impact on the dynamics are also identified. These outcomes are pivotal for refining and optimizing the proposed system to enhance its predictive accuracy and efficacy in modeling tumor behavior. [ABSTRACT FROM AUTHOR]

Combination antiretroviral Therapy (cART) is the standard treatment approach for human immunodeficiency virus (HIV), involving the use of various antiretroviral drugs to effectively suppress the virus’s replication in the body. The objective of cART is to decrease the viral load in the blood to undetectable levels, enhance the immune system’s function, and ultimately prolong the patient’s life by preventing the progression to AIDS and associated opportunistic infections. In this work, we formulated the dynamics of HIV infection, including the effects of cART, within a fractional framework. This paper presents a numerical study that investigates the complex dynamics of HIV infection in CD4+\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\text {CD4}^{+}$$\end{document} T cells. The proposed HIV model incorporates the impact of antiretroviral medication via the Caputo–Fabrizio derivative. To comprehend the dynamics of the proposed HIV infection model, a numerical approach is employed. The dynamic behavior of the system is illustrated by examining the influence of various input parameters, aiming to capture the system’s sensitivity to these factors. Furthermore, this modeling approach highlights the interaction between the immune system and the virus. Through numerical simulations utilizing specific input values, we explore the chaotic and periodic behavior of HIV infection and provide insights into its intricate dynamics. [ABSTRACT FROM AUTHOR]

In this article, we investigate a tumor-immune and antigen-presenting cells population in the form of a mathematical model. To achieve greater accuracy in understanding the spread of tumor and immune cell populations, we apply the Caputo–Fabrizio (CF) fractional-order derivative. The fixed-point theorems are employed to analyze the uniqueness and existence of the model. The Laplace transform along with the Adomian decomposition approach is used to construct an algorithm for a semi-analytical solution under the CF fractional derivative. The chaotic dynamics of the cancer-immune model are confirmed by the Lyapunov exponents. The article examines how different vaccination protocols can affect tumor dormancy and recurrence. Furthermore, we offer a description for why adoptive immunotherapy techniques may potentially increase tumor growth rather than suppress it. [ABSTRACT FROM AUTHOR]

Farmers are trying to adopt new cultivation methods and technologies to produce more and good yield. Low productivity is due to a variety of factors; one of the main reasons is the existence of plant diseases spread by insects and pathogens. Infection in the plants of red chilli via the yellow virus is a current issue for the farmers. Here, we construct a model for the propagation of the yellow virus in the plants of red chilli to investigate the key factors. The proposed model is then presented in the framework of fractional derivative for more accurate findings. By applying the method of next-generation matrix, we determine the basic reproduction number R 0 . The recommended model is investigated for biological meaningful results. Moreover, we focus on the dynamical behavior and qualitative analysis of the yellow virus infection in the plants of red chili. Schaefer and Banach fixed-point theorems are utilized to demonstrate the uniqueness and existence of the solution of the recommended system. We find suitable circumstances for the Ulam–Hyers stability of the recommended system of plants infection. The solution routes are examined using a unique numerical method to highlight the contribution of the input factors on yellow virus dynamics. Key factors of the system are investigated numerically through different simulations. The most critical factors of the infection are highlighted to the policymakers for the prevention of the losses. [ABSTRACT FROM AUTHOR]