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In this paper, we investigate a scenario concerning a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. By establishing suitable conditions, we have proved that a finite-time blow-up occurs in the solution. [ABSTRACT FROM AUTHOR]

The current study investigates the two-dimensional incompressible viscous flow of CNTs (carbon nanotube) blood base hybrid nanofluids, both multi wall and single wall, with the considered impact of MHD, couple stress, Marangoni convection, thermal radiation and viscous dissipation. Appropriate similarity transformation is used to convert the governing flow problem partial differential equation to dimensionless nonlinear ordinary differential equations. We solve this dimensionless coupled equation, one for temperature and one for velocity, using the homotopy analysis method (HAM). The flow characteristics, such as temperature and velocity profiles, are studied and simulated using a physical description in response to changes in developing factors. Based on the data presented, it can be concluded that CNT is a more dependable material for industrial and technological applications due to its superior heat transfer properties. For hybrid nanofluids, a decrease in the temperature curve is observed with increasing prandtl number and enhancement with the increasing value of thermal radiation, viscous dissipation and temperature ratio factors. By enhancing the volume friction parameter, coupling stress parameter and magnetic parameter increase, the hybrid nanofluid velocity curve falls. This paper also investigates the blood-based hybrid nanofluid's thermal performance as measured by the local skin friction coefficient and Nusselt number. The major outcome of this research work is to increase the effectiveness of heat exchangers, cooling systems and thermal management equipment. It improved heat transfer capability results from the base fluid's increased thermal conductivity. [ABSTRACT FROM AUTHOR]

This study examines the impact of viscous dissipation past a fluctuating disk on the three-dimensional unsteady incompressible viscous flow of water-based nanofluids. The problem's mathematical modeling entails the formulation of continuity, momentum, and energy equations—three fundamental nonlinear governing equations. The proper transformations were conducted in order to convert a collection of partial differential equations (PDEs) to nonlinear ordinary differential equations (NODEs). The obtained governing equations are then solved analytically using the homotopy analysis method (HAM). The study looks into the effects of many factors. To illustrate the influence of these characteristics, the study displays temperature filed and velocity filed as graphical representations. It is anticipated that this work will progress the field of condensed nanostructure and nanomaterials, providing new directions for future investigation in applications pertaining to heat transfer enhancement. [ABSTRACT FROM AUTHOR]

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, distributed delay, and variable exponents. Under a suitable hypothesis the blow-up and growth of solutions are proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case of absence of the source term f 1 = f 2 = 0 . [ABSTRACT FROM AUTHOR]

We examine a Kirchhoff-type equation with nonlinear viscoelastic properties, characterized by distributed delay, logarithmic nonlinearity, and Balakrishnan–Taylor damping terms (elastic membrane equation). Under appropriate hypotheses, we establish the occurrence of solution blow-up. [ABSTRACT FROM AUTHOR]

The complex fuzzy sets, complex intuitionistic fuzzy sets, complex pythagorean fuzzy sets, and complex fermatean fuzzy sets cannot handle the neutrality grade of an object that plays an important role in medical diagnosis, network analysis, signal processing, human voting, and personnel selection problems. Therefore, in this article, we introduced the notion of complex picture fuzzy sets and investigated their basic properties. The complex picture fuzzy sets are effective and powerful tools for many ambiguous and uncertain problems. Distance measures play an essential role in establishing a useful link from the expression of imprecise and uncertain information to various real life applications, including machine learning, market predictions, decision-making processes, clustering, and pattern recognition. Therefore, in this study, we developed some measures of distances under complex picture fuzzy environments. Finally, we developed an algorithm using complex picture fuzzy environments and applied it to a practical application concerning decision making, medical diagnosis, and pattern recognition problems. [ABSTRACT FROM AUTHOR]

This work investigates the well-posedness and stability outcomes of the one-dimensional Cauchy problem within a system involving swelling-porous elastic soils and thermal effects. The heat conduction in this system is described by the Lord–Shulman theory. By the energy method, we establish the existence of solutions and then prove an exponential stability result under suitable hypotheses. Our results were achieved without the need for the condition of equal velocities, and it is also considered a good improvement to our work in the paper (Choucha et al. in Mathematics 11(23):4785, 2023), completely dispensing with any damping term. [ABSTRACT FROM AUTHOR]

In this work, we deal with a one-dimensional Cauchy problem in Timoshenko system with temperature and microtemperature effect. The heat conduction is given by the theory of Lord–Shulman. We prove that the dissipation induced by the coupling of the Timoshenko system with the heat conduction of Lord–Shulman’s theory alone is strong enough to stabilize the system, but with slow decay rate. To show our result, we transform our system into a first order system and, applying the energy method in the Fourier space, we establish some pointwise estimates of the Fourier image of the solution. Using those pointwise estimates, we prove the decay estimates of the solution and show that those decay estimates are very slow, we prove our main result under suitable assumption. [ABSTRACT FROM AUTHOR]

The burden of vector-borne infections is significant, particularly in low- and middle-income countries where vector populations are high and healthcare infrastructure may be inadequate. Further, studies are required to investigate the key factors of vector-borne infections to provide effective control measure. This study focuses on formulating a mathematical framework to characterize the spread of chikungunya infection in the presence of vaccines and treatments. The research is primarily dedicated to descriptive study and comprehension of dynamic behaviour of chikungunya dynamics. We use Banach's and Schaefer's fixed point theorems to investigate the existence and uniqueness of the suggested chikungunya framework resolution. Additionally, we confirm the Ulam–Hyers stability of the chikungunya system. To assess the impact of various parameters on the dynamics of chikungunya, we examine solution pathways using the Laplace-Adomian method of disintegration. Specifically, to visualise the impacts of fractional order, vaccination, bite rate and treatment computer algorithms are employed on the infection level of chikungunya. Our research identified the framework's essential input settings for managing chikungunya infection. Notably, the intensity of chikungunya infection can be reduced by lowering mosquito bite rates in the affected area. On the other hand, vaccination, memory index or fractional order, and treatment could be used as efficient controlling variables. [ABSTRACT FROM AUTHOR]

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.

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]

The decay rate of solutions to a Bresse system in thermoelasticity of type III with respect to the distributed delay term is the subject of this study. We demonstrate our major finding utilising the energy approach in the Fourier space. [ABSTRACT FROM AUTHOR]

The infection of lymphatic filariasis (LF) is the primary cause of poverty and disability in individuals living with the disease. Many organizations globally are working toward mitigating the disease's impact and enhancing the quality of life of the affected patients. It is paramount to inspect the transmission pattern of this infection to provide effective interventions for its prevention and control. Here, we formulate an epidemic model for the progression process of LF with acute and chronic infection in the fractional framework. The basic concept of the novel Atangana-Baleanu operator is presented for the analysis of suggested system. We determine the basic reproduction number of the system via the approach of next-generation matrix and investigate the equilibria of the system for stability analysis. We have shown the impact of input factors on the outcomes of reproduction parameter with the help of partial rank correlation coefficient approach and visualize the most critical factors. To conceptualize the time series analysis of the suggested dynamics, we propose utilizing a numerical approach. The solution pathways of the system are illustrated to demonstrate how different settings affect the system. We demonstrate the dynamics of the infection numerically to educate the policy makers and health authorities about the mechanisms necessary for management and control. [ABSTRACT FROM AUTHOR]

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]

Pulse vaccination is a repeated vaccination policy, which plays a tremendous role in the global fight against communicable diseases in terms of saving medical resources and decreasing the economic burden. In this article, we propose a dynamic model of dengue infection with periodic transmission functions and seasonality in vector population. Furthermore, we introduce a pulse vaccination strategy in the susceptible host population to examine how frequency and intensity of implementation of this strategy affect the dynamics of dengue infection. We successfully obtained the threshold dynamics by defining the basic reproduction number R0, which is the spectral radius of the next generation operator and governs whether the disease dies out or not. It has been established that the infection-free periodic solution of the proposed impulsive system is globally asymptotically stable if R 0 < 1 and is unstable otherwise. Moreover, we found that the dengue infection is uniformly persistent for the proposed system if R 0 > 1 . Finally, we execute the system numerically to illustrate the piecewise solutions of the proposed system with impulsive vaccination measure and to investigate the influence of different control parameters on the basic reproduction. The finding indicates that a frequent implementation of the vaccination strategy with great intensity and the use of mosquito nets can essentially lead to a decline of new infections. [ABSTRACT FROM AUTHOR]