Analytical solutions for the Noyes Field model of the time fractional Belousov Zhabotinsky reaction using a hybrid integral transform technique.

In this work, we employed an attractive hybrid integral transform technique known as the natural transform decomposition method (NTDM) to investigate analytical solutions for the Noyes-Field (NF) model of the time-fractional Belousov-Zhabotinsky (TF-BZ) reaction system. The aforementioned time-fractional model is considered within the framework of the Caputo, Caputo-Fabrizio, and Atangana-Baleanu fractional derivatives. The NTDM couples the Adomian decomposition method and the natural transform method to generate rapidly convergent series-type solutions via an elegant iterative approach.

Retraction notice to "Analysis of Conocurvone, Ganoderic acid A and Oleuropein molecules against the main protease molecule of COVID-19 by in silico approaches: Molecular dynamics docking studies" [Engineering Analysis with Boundary Elements volume 150 (2023) Pages 583-598].

[This retracts the article DOI: 10.1016/j.enganabound.

Analyzing solitary wave solutions of the nonlinear Murray equation for blood flow in vessels with non-uniform wall properties.

Solitary wave solutions are of great interest to bio-mathematicians and other scientists because they provide a basic description of nonlinear phenomena with many practical applications. They provide a strong foundation for the development of novel biological and medical models and therapies because of their remarkable behavior and persistence. They have the potential to improve our comprehension of intricate biological systems and help us create novel therapeutic approaches, which is something that researchers are actively investigating.

Stability Analysis of SARS-CoV-2 with Heart Attack Effected Patients and Bifurcation.

The aim of this study is to analyze and investigate the SARS-CoV-2 (SC-2) transmission with effect of heart attack in United Kingdom with advanced mathematical tools. Mathematical model is converted into fractional order with the help of fractal fractional operator (FFO). The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position.

Similarity analysis of bioconvection of unsteady nonhomogeneous hybrid nanofluids influenced by motile microorganisms.

Motile bacteria in hybrid nanofluids cause bioconvection. Bacillus cereus, Pseudomonas viscosa, Bacillus brevis, Salmonella typhimurium, and Pseudomonas fluorescens were used to evaluate their effect and dispersion in the hybrid nanofluid. Using similarity analysis, a two-phase model for mixed bioconvection magnetohydrodynamic flow was developed using hybrid nanoparticles of AlO and Cu (Cu-AlO/water).

The analysis of a new fractional model to the Zika virus infection with mutant.

We present a new mathematical model to analyze the dynamics of the Zika virus (ZV) disease with the mutant under the real confirmed cases in Colombia. We give the formulation of the model initially in integer order derivative and then extend it to a fractional order system in the sense of the Mittag-Leffler kernel. We study the properties of the model in the Mittag-Leffler kernel and establish the result.

A dynamical study on stochastic reaction diffusion epidemic model with nonlinear incidence rate.

The current study deals with the stochastic reaction-diffusion epidemic model numerically with two proposed schemes. Such models have many applications in the disease dynamics of wildlife, human life, and others. During the last decade, it is observed that the epidemic models cannot predict the accurate behavior of infectious diseases.

Analysis of Conocurvone, Ganoderic acid A and Oleuropein molecules against the main protease molecule of COVID-19 by approaches: Molecular dynamics docking studies.

Traditional medicines against COVID-19 have taken important outbreaks evidenced by multiple cases, controlled clinical research, and randomized clinical trials. Furthermore, the design and chemical synthesis of protease inhibitors, one of the latest therapeutic approaches for virus infection, is to search for enzyme inhibitors in herbal compounds to achieve a minimal amount of side-effect medications. Hence, the present study aimed to screen some naturally derived biomolecules with anti-microbial properties (anti-HIV, antimalarial, and anti-SARS) against COVID-19 by targeting coronavirus main protease via molecular docking and simulations.

Numerical investigation of treated brain glioma model using a two-stage successive over-relaxation method.

A brain tumor is a dynamic system in which cells develop rapidly and abnormally, as is the case with most cancers. Cancer develops in the brain or inside the skull when aberrant and odd cells proliferate in the brain. By depriving the healthy cells of leisure, nutrition, and oxygen, these aberrant cells eventually cause the healthy cells to perish.

Connecting in Silicate and Silicate Chain Networks to Compute Kulli Temperature Indices.

A topological index is a numerical parameter that is derived mathematically from a graph structure. In chemical graph theory, these indices are used to quantify the chemical properties of chemical compounds. We compute the first and second temperature, hyper temperature indices, the sum connectivity temperature index, the product connectivity temperature index, the reciprocal product connectivity temperature index and the F temperature index of a molecular graph silicate network and silicate chain network.

Mathematical modeling of corona virus (COVID-19) and stability analysis.

In this paper, the mathematical modeling of the novel corona virus (COVID-19) is considered. A brief relationship between the unknown hosts and bats is described. Then the interaction among the seafood market and peoples is studied.

Analysis and Simulation of Fractional Order Smoking Epidemic Model.

In recent years, there are many new definitions that were proposed related to fractional derivatives, and with the help of these definitions, mathematical models were established to overcome the various real-life problems. The true purpose of the current work is to develop and analyze Atangana-Baleanu (AB) with Mittag-Leffler kernel and Atangana-Toufik method (ATM) of fractional derivative model for the Smoking epidemic. Qualitative analysis has been made to `verify the steady state.

A delayed plant disease model with Caputo fractional derivatives.

We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model.

A new fuzzy fractional order model of transmission of Covid-19 with quarantine class.

This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized, and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo's sense.

Construction of optical solitons of magneto-optic waveguides with anti-cubic law nonlinearity.

Two efficient integration schemes, new extended hyperbolic function and generalized tanh are employed to discover optical soliton solutions to magneto-optic waveguides that retains anti-cubic form of nonlinear refractive index. Bright, dark, periodic singular, singular, and combo soliton solutions have created. These solutions expose the comprehensive variety of soliton solutions.

Analysis of fractional COVID-19 epidemic model under Caputo operator.

The article deals with the analysis of the fractional COVID-19 epidemic model (FCEM) with a convex incidence rate. Keeping in view the fading memory and crossover behavior found in many biological phenomena, we study the coronavirus disease by using the noninteger Caputo derivative (CD). Under the Caputo operator (CO), existence and uniqueness for the solutions of the FCEM have been analyzed using fixed point theorems.

Analysis of novel fractional COVID-19 model with real-life data application.

The current work is of interest to introduce a detailed analysis of the novel fractional COVID-19 model. Non-local fractional operators are one of the most efficient tools in order to understand the dynamics of the disease spread. For this purpose, we intend as an attempt at investigating the fractional COVID-19 model through Caputo operator with order .

Fractional methicillin-resistant infection model under Caputo operator.

This study provides a detailed exposition of in-hospital community-acquired methicillin-resistant (CA-MRSA) which is a new strain of MRSA, and hospital-acquired methicillin-resistant (HA-MRSA) employing Caputo fractional operator. These two strains of MRSA, referred to as staph, have been a serious problem in hospitals and it is known that they give rise to more deaths per year than AIDS. Hence, the transmission dynamics determining whether the CA-MRSA overtakes HA-MRSA is analyzed by means of a non-local fractional derivative.

Modeling of pressure-volume controlled artificial respiration with local derivatives.

We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated -derivative and proportional derivative.

Existence, uniqueness, and stability of fractional hepatitis B epidemic model.

This paper describes the existence and stability of the hepatitis B epidemic model with a fractional-order derivative in Atangana-Baleanu sense. Some new results are handled by using the Sumudu transform. The existence and uniqueness of the equilibrium solution are presented using the Banach fixed-point theorem.

Stability analysis of leishmania epidemic model with harmonic mean type incidence rate.

We discussed anthroponotic cutaneous leishmania transmission in this article, due to its large effect on the community in the recent years. The mathematical model is developed for anthroponotic cutaneous leishmania transmission, and its qualitative behavior is taken under consideration. The threshold number of the model is derived using the next-generation method.

Mathematical modeling for adsorption process of dye removal nonlinear equation using power law and exponentially decaying kernels.

In this research work, a new time-invariant nonlinear mathematical model in fractional (non-integer) order settings has been proposed under three most frequently employed strategies of the classical Caputo, the Caputo-Fabrizio, and the Atangana-Baleanu-Caputo with the fractional parameter χ, where 0<χ≤1. The model consists of a nonlinear autonomous transport equation used to study the adsorption process in order to get rid of the synthetic dyeing substances from the wastewater effluents. Such substances are used at large scale by various industries to color their products with the textile and chemical industries being at the top.

Solutions of a disease model with fractional white noise.

We consider an epidemic disease system by an additive fractional white noise to show that epidemic diseases may be more competently modeled in the fractional-stochastic settings than the ones modeled by deterministic differential equations. We generate a new SIRS model and perturb it to the fractional-stochastic systems. We study chaotic behavior at disease-free and endemic steady-state points on these systems.

Fractional modeling of blood ethanol concentration system with real data application.

In this study, a physical system called the blood ethanol concentration model has been investigated in its fractional (non-integer) order version. The three most commonly used fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu fractional derivative in the Caputo sense-ABC and the Caputo-Fabrizio-CF) kernels have been used to fractionalize the model, whereas during the process of fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique.