Exploring optical solitary wave solutions in the (2+1)-dimensional equation with in-depth of dynamical assessment.

The current study explores the (2+1)-dimensional Chaffee-Infante equation, which holds significant importance in theoretical physics renowned reaction-diffusion equation with widespread applications across multiple disciplines, for example, ion-acoustic waves in optical fibres, fluid dynamics, electromagnetic wave fields, high-energy physics, coastal engineering, fluid mechanics, plasma physics, and various other fields. Furthermore, the Chaffee-Infante equation serves as a model that elucidates the physical processes of mass transport and particle diffusion. We employ an innovative new extended direct algebraic method to enhance the accuracy of the derived exact travelling wave solutions. The obtained soliton solutions span a wide range of travelling waves like bright-bell shape, combined bright-dark, multiple bright-dark, bright, flat-kink, periodic, and singular. These solutions offer valuable insights into wave behaviour in nonlinear media and find applications in diverse fields such as optical fibres, fluid dynamics, electromagnetic wave fields, high-energy physics, coastal engineering, fluid mechanics, and plasma physics. Soliton solutions are visually present by manipulating parameters using Wolfram Mathematica software, graphical representations allow us to study solitary waves as parameters change. Observing the dynamics of the model, this study presents sensitivity in a nonlinear dynamical system. The applied mathematical approaches demonstrate its ability to identify reliable and efficient travelling wave solitary solutions for various nonlinear evolution equations.

Computational study of effect of hybrid nanoparticles on hemodynamics and thermal transfer in ruptured arteries with pathological dilation.

The intended research aims to explore the convection phenomena of a hybrid nanofluid composed of gold and silver nanoparticles. This research is novel and significant because there is a lack of existing studies on the flow behavior of hybrid nanoparticles with important physical properties of blood base fluids, especially in the case of sidewall ruptured dilated arteries. The implementation of combined nanoparticles rather than unadulterated nanoparticles is one of the most crucial elements in boosting the thermal conduction of fluids. The research methodology encompasses the utilization of advanced bio-fluid dynamics software for simulating the flow of the nanofluid. The physical context elucidates the governing equations of momentum, mass, momentum, and energy in terms of partial differential equations. The results are displayed in both tabular and graphical forms to demonstrate the numerical and graphical solutions. The effect of physical parameters on velocity distribution is illustrated through graphs. Furthermore, the study's findings are unique and original, and these computational discoveries have not been published by any researcher before. The finding implies that utilizing hybrid nanoparticles as drug carriers holds great promise in mitigating the effects of blood flow, potentially enhancing drug delivery, and minimizing its impact on the body.

Computation of soliton structure and analysis of chaotic behaviour in quantum deformed Sinh-Gordon model.

Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed modified auxiliary and new direct extended algebraic methods. Trigonometric, hyperbolic, exponential and rational solutions are successfully extracted using these techniques, coupled with the best possible constraint requirements implemented on parameters to ensure the existence of solutions. The findings, then, are represented by 2D, 3D and contour plots to highlight the various solitons' propagation patterns such as kink-bright, bright, dark, bright-dark, kink, and kink-peakon solitons and solitary wave solutions. It is worth emphasizing that kink dark, dark peakon, dark and dark bright solitons have not been found earlier in literature. In phase 2, the underlying model is examined under various chaos detecting tools for example lyapunov exponents, multistability and time series analysis and bifurcation diagram. Chaotic behavior is investigated using various initial condition and novel results are obtained.

A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling.

In survival and stochastic lifespan modeling, numerous families of distributions are sometimes considered unnatural, unjustifiable theoretically, and occasionally superfluous. Here, a novel parsimonious survival model is developed using the Bilal distribution (BD) and the Kavya-Manoharan (KM) parsimonious transformation family. In addition to other analytical properties, the forms of probability density function (PDF) and behavior of the distributions' hazard rates are analyzed. The insights are theoretical as well as practical. Theoretically, we offer explicit equations for the single and product moments of order statistics from Kavya-Manoharan Bilal Distribution. Practically, maximum likelihood (ML) technique, which is based on simple random sampling (SRS) and ranked set sampling (RSS) sample schemes, is employed to estimate the parameters. Numerical simulations are used as the primary methodology to compare the various sampling techniques.

A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs.

This article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if their product results in zero (x.y=0). The set of zero divisors in ring R is referred to as L(R). To analyze various algebraic properties of R, a graph known as the zero-divisor graph is constructed using L(R). This manuscript establishes specific general bounds for the dominant metric dimension (Ddim) concerning the ZD-graph of R. To achieve this objective, we examine the zero divisor graphs for specific rings, such as the ring of Gaussian integers modulo m, denoted as Zm[i], the ring of integers modulo n, denoted as Zn, and some quotient polynomial rings. Our research unveils new insights into the structural similarities and differences among commutative rings sharing identical metric dimensions and dominant metric dimensions. Additionally, we present a general result outlining bounds for the dominant metric dimension expressed in terms of the maximum degree, girth, clique number, and diameter of the associated ZD-graphs. Through this exploration, we aim to provide a comprehensive framework for analyzing commutative rings and their associated zero divisor graphs, thereby advancing both theoretical knowledge and practical applications in diverse domains.

A novel probabilistic q-rung orthopair linguistic neutrosophic information-based method for rating nanoparticles in various sectors.

The idea of probabilistic q-rung orthopair linguistic neutrosophic (P-QROLN) is one of the very few reliable tools in computational intelligence. This paper explores a significant breakthrough in nanotechnology, highlighting the introduction of nanoparticles with unique properties and applications that have transformed various industries. However, the complex nature of nanomaterials makes it challenging to select the most suitable nanoparticles for specific industrial needs. In this context, this research facilitate the evaluation of different nanoparticles in industrial applications. The proposed framework harnesses the power of neutrosophic logic to handle uncertainties and imprecise information inherent in nanoparticle selection. By integrating P-QROLN with AO, a comprehensive and flexible methodology is developed for assessing and ranking nanoparticles according to their suitability for specific industrial purposes. This research contributes to the advancement of nanoparticle selection techniques, offering industries a valuable tool for enhancing their product development processes and optimizing performance while minimizing risks. The effectiveness of the proposed framework are demonstrated through a real-world case study, highlighting its potential to revolutionize nanoparticle selection in HVAC (Heating, Ventilation, and Air Conditioning) industry. Finally, this study is crucial to enhance nanoparticle selection in industries, offering a sophisticated framework probabilistic q-rung orthopair linguistic neutrosophic quantification with an aggregation operator to meet the increasing demand for precise and informed decision-making.

Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks.

The primary objective of this research is to develop a mathematical model, analyze the dynamic occurrence of thermal shock and exploration of how thermal memory with moving line impact of heat transfer within biological tissues. An extended version of the Pennes equation as its foundational framework, a new fractional modelling approach called the Prabhakar fractional operator to investigate and a novel time-fractional interpretation of Fourier's law that incorporates its historical behaviour. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fractional formulation of heat flow, achieved through a generalized fractional operator with a non-singular type kernel, enables the representation of the finite propagation speed of heat waves. Furthermore, the dynamics of thermal source continually generates a linear thermal shock at predefined locations within the tissue. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also expressed the solution in the form of special functions. The article derives analytical solutions for the heat transfer phenomena of both the generalized model, in the Laplace domain, and the ordinary model in the real domain, employing Laplace inverse transformation. The pertinent parameter's influence, such as α, ß, γ, a0, b0, to gain insights into the impact of the thermal memory parameter on heat transfer, is brought under consideration to reveal the interesting results with graphical representations of the findings.

Numerical simulation of a fractional stochastic delay differential equations using spectral scheme: a comprehensive stability analysis.

The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time delays. The purpose of this study is to explore the stability analysis of a system of FSDDEs. Our study emphasizes the interaction between fractional calculus, stochasticity, and time delays in understanding the stability of such systems. Analyzing the moments of the system's solutions, we investigate stochasticity's influence on FSDDS. The article provides practical insight into solving FSDDS efficiently using various numerical techniques. Additionally, this research focuses both on asymptotic as well as Lyapunov stability of FSDDS. The local stability conditions are clearly presented and also the effects of a fractional orders with delay on the stability properties are examine. Through a comprehensive test of a stability criteria, practical examples and numerical simulations we demonstrate the complexity and challenges concern with the analyzing FSDDEs.

Modeling and analysis of hybrid-blood nanofluid flow in stenotic artery.

Current communication deals with the flow impact of blood inside cosine shape stenotic artery. The under consideration blood flow is treated as Newtonian fluid and flow is assumed to be two dimensional. The governing equation are modelled and solved by adopting similarity transformation under the stenosis assumptions. The important quantities like Prandtl number, flow parameter, blood flow rate and skin friction are attained to analyze the blood flow phenomena in stenosis. The variations of different parameters have been shown graphically. It is of interest to note that velocity increases due to change in flow parameter gamma and temperature of blood decreases by increasing nanoparticles volume fraction and Prandtl number. In the area of medicine, the most interesting nanotechnology approach is the nanoparticles applications in chemotherapy. This study provides further motivation to include more convincing consequences in the present model to represent the blood rheology.

Global dynamics and computational modeling approach for analyzing and controlling of alcohol addiction using a novel fractional and fractal-fractional modeling approach.

In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal-fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal-fractional alcohol addiction model are shown using the Picard-Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam-Hyers coupled with the Ulam-Hyers-Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community.

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. The basic reproduction of the fractional system is computed. The equilibrium points of the Zika virus model are obtained and found that the endemic equilibria exist when the threshold is greater than unity. Further, we show that the model does not possess the backward bifurcation phenomenon. The numerical procedure to solve the problem using the Atangana-Baleanu derivative is shown using the newly established numerical scheme. We consider the real cases of the Zika virus in Colombia outbreak are considered and simulate the model using the nonlinear least square curve fit and computed the basic reproduction number R0=0.4942, whereas in previous work (Alzahrani et al., 2021) [1], the authors computed the basic reproduction number R0=0.5447. This is due to the fact that our work in the present paper provides better fitting to the data when using the fractional order model, and indeed the result regarding the data fitting using the fractional model is better than integer order model. We give a sensitivity analysis of the parameters involved in the basic reproduction number and show them graphically. The results obtained through the present numerical method converge to its equilibrium for the fractional order, indicating the proposed scheme's reliability.

An efficient spline technique for solving time-fractional integro-differential equations.

Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability to approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal of this study is to use extended cubic B-spline (ExCuBS) functions with a new second order derivative approximation to obtain the numerical solution of the weakly singular kernel (SK) non-linear fractional partial integro-differential equation (FPIDE). The spatial and temporal fractional derivatives are discretized by ExCuBS and the Caputo finite difference scheme, respectively. The present study found that it is stable and convergent. The validity of the current approach is examined on a few test problems, and the obtained outcomes are compared with those that have previously been reported in the literature.

A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques.

In this paper, a new spatio-temporal model is formulated to study the spread of coronavirus infection (COVID-19) in a spatially heterogeneous environment with the impact of vaccination. Initially, a detailed qualitative analysis of the spatio-temporal model is presented. The existence, uniqueness, positivity, and boundedness of the model solution are investigated. Local asymptotical stability of the diffusive COVID-19 model at steady state is carried out using well-known criteria. Moreover, a suitable nonlinear Lyapunov functional is constructed for the global asymptotical stability of the spatio-temporal model. Further, the model is solved numerically based on uniform and non-uniform initial conditions. Two different numerical schemes named: finite difference operator-splitting and mesh-free operator-splitting based on multi-quadratic radial basis functions are implemented in the numerical study. The impact of diffusion as well as some pharmaceutical and non-pharmaceutical control measures, i.e., reducing an effective contact causing infection transmission, vaccination rate and vaccine waning rate on the disease dynamics is presented in a spatially heterogeneous environment. Furthermore, the impact of the  aforementioned interventions is investigated with and without diffusion on the incidence of disease. The simulation results conclude that the random motion of individuals has a significant impact on the disease dynamics and helps in setting a better control strategy for disease eradication.

Further study of eccentricity based indices for benzenoid hourglass network.

Topological Indices are the mathematical estimate related to atomic graph that corresponds biological structure with several real properties and chemical activities. These indices are invariant of graph under graph isomorphism. If top(h1) and top(h2) denotes topological index h1 and h2 respectively then h1 approximately equal h2 which implies that top(h1) = top(h2). In biochemistry, chemical science, nano-medicine, biotechnology and many other science's distance based and eccentricity-connectivity(EC) based topological invariants of a network are beneficial in the study of structure-property relationships and structure-activity relationships. These indices help the chemist and pharmacist to overcome the shortage of laboratory and equipment. In this paper we calculate the formulas of eccentricity-connectivity descriptor(ECD) and their related polynomials, total eccentricity-connectivity(TEC) polynomial, augmented eccentricity-connectivity(AEC) descriptor and further the modified eccentricity-connectivity(MEC) descriptor with their related polynomials for hourglass benzenoid network.

Unsteady hybrid nanofluid (Cu-UO2/blood) with chemical reaction and non-linear thermal radiation through convective boundaries: An application to bio-medicine.

This study is focused on modeling and simulations of hybrid nanofluid flow. Uranium dioxide UO2 nanoparticles are hybrid with copper Cu, copper oxide CuO and aluminum oxide Al2O3 while considering blood as a base fluid. The blood flow is initially modeled considering magnetic effect, non-linear thermal radiation and chemical reactions along with convective boundaries. Then for finding solution of the obtained highly nonlinear coupled system we propose a methodology in which q-homotopy analysis method is hybrid with Galerkin and least square Optimizers. Residual errors are also computed in this study to confirm the validity of results. Analysis reveals that rate of heat transfer in arteries increases up to 13.52 Percent with an increase in volume fraction of Cu while keeping volume fraction of UO2 fixed to 1% in a base fluid (blood). This observation is in excellent agreement with experimental result. Furthermore, comparative graphical study of Cu,CuO and Al2O3 for increasing volume fraction is also performed keeping UO2 volume fraction fixed. Investigation indicates that Cu has the highest rate of heat transfer in blood when compared with CuO and Al2O3. It is also observed that thermal radiation increases the heat transfer rate in the current study. Furthermore, chemical reaction decreases rate of mass transfer in hybrid blood nanoflow. This study will help medical practitioners to minimize the adverse effects of UO2 by introducing hybrid nano particles in blood based fluids.

Analysis of blood flow of unsteady Carreau-Yasuda nanofluid with viscous dissipation and chemical reaction under variable magnetic field.

Blood flow analysis through arterial walls depicts unsteady non-Newtonian fluid flow behavior. Arterial walls are impacted by various chemical reactions and magnetohydrodynamic effects during treatment of malign and tumors, cancers, drug targeting and endoscopy. In this regard, current manuscript focuses on modeling and analysis of unsteady non-Newtonian Carreau-Yasuda fluid with chemical reaction, Brownian motion and thermophoresis under variable magnetic field. The main objective is to simulate the effect of different fluid parameters, especially variable magnetic field, chemical reaction and viscous dissipation on the blood flow to help medical practitioners in predicting the changes in blood to make diagnosis and treatment more efficient. Suitable similarity transformations are used for the conversion of partial differential equations into a coupled system of ordinary differential equations. Homotopy analysis method is used to solve the system and convergent results are drawn. Effect of different dimensionless parameters on the velocity, temperature and concentration profiles of blood flow are analyzed in shear thinning and thickening cases graphically. Analysis reveals that chemical reaction increases blood concentration which enhance the drug transportation. It is also observed that magnetic field elevates the blood flow in shear thinning and thickening scenarios. Furthermore, Brownian motion and thermophoresis increases temperature profile.

Investigating regulated signaling pathways in therapeutic targeting of non-small cell lung carcinoma.

Non-small cell lung carcinoma (NSCLC) is the most common malignancy worldwide. The signaling cascades are stimulated via genetic modifications in upstream signaling molecules, which affect apoptotic, proliferative, and differentiation pathways. Dysregulation of these signaling cascades causes cancer-initiating cell proliferation, cancer development, and drug resistance. Numerous efforts in the treatment of NSCLC have been undertaken in the past few decades, enhancing our understanding of the mechanisms of cancer development and moving forward to develop effective therapeutic approaches. Modifications of transcription factors and connected pathways are utilized to develop new treatment options for NSCLC. Developing designed inhibitors targeting specific cellular signaling pathways in tumor progression has been recommended for the therapeutic management of NSCLC. This comprehensive review provided deeper mechanistic insights into the molecular mechanism of action of various signaling molecules and their targeting in the clinical management of NSCLC.

Heat and mass flux analysis of magneto-free-convection flow of Oldroyd-B fluid through porous layered inclined plate.

The present work examines the analytical solutions of the double duffusive magneto free convective flow of Oldroyd-B fluid model of an inclined plate saturated in a porous media, either fixed or moving oscillated with existence of slanted externally magnetic field. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimensional form. On the fluid velocity, the influence of different angles that plate make with vertical is studied as well as slanted angles of the electro magnetic lines with the porous layered inclined plate are also discussed, associated with thermal conductivity and constant concentration. For seeking exact solutions in terms of special functions namely Mittag-Leffler functions, G-function etc., for Oldroyd-B fluid velocity, concentration and Oldroyd-B fluid temperature, Laplace integral transformation method is used to solve the non-dimensional model. The contribution of different velocity components are considered as thermal, mass and mechanical, and analyse the impacts of these components on the fluid dynamics. For several physical significance of various fluidic parameters on Oldroyd-B fluid velocity, concentration and Oldroyd-B fluid temperature distributions are demonstrated through various graphs. Furthermore, for being validated the acquired solutions, some limiting models such as Newtonian fluid in the absence of different fluidic parameters. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work and studied various cases regarding the movement of plate.

Thermo diffusion impacts on the flow of second grade fluid with application of (ABC), (CF) and (CPC) subject to exponential heating.

The aim of this article is to investigate the exact solution by using a new approach for the thermal transport phenomena of second grade fluid flow under the impact of MHD along with exponential heating as well as Darcy's law. The phenomenon has been expressed in terms of partial differential equations, then transformed the governing equations in non-dimentional form. For the sake of better rheology of second grade fluid, developed a fractional model by applying the new definition of Constant Proportional-Caputo hybrid derivative (CPC), Atangana Baleanu in Caputo sense (ABC) and Caputo Fabrizio (CF) fractional derivative operators that describe the generalized memory effects. For seeking exact solutions in terms of Mittag-Leffler and G-functions for velocity, temperature and concentration equations, Laplace integral transformation technique is applied. For physical significance of various system parameters on fluid velocity, concentration and temperature distributions are demonstrated through various graphs by using graphical software. Furthermore, for being validated the acquired solutions, accomplished a comparative analysis with some published work. It is also analyzed that for exponential heating and non-uniform velocity conditions, the CPC fractional operator is the finest fractional model to describe the memory effect of velocity, energy and concentration profile. Moreover, the graphical representations of the analytical solutions illustrated the main results of the present work. Also, in the literature, it is observed that to derived analytical results from fractional fluid models developed by the various fractional operators, is difficult and this article contributing to answer the open problem of obtaining analytical solutions the fractionalized fluid models.

Application of piecewise fractional differential equation to COVID-19 infection dynamics.

We proposed a new mathematical model to study the COVID-19 infection in piecewise fractional differential equations. The model was initially designed using the classical differential equations and later we extend it to the fractional case. We consider the infected cases generated at health care and formulate the model first in integer order. We extend the model into Caputo fractional differential equation and study its background mathematical results. We show that the fractional model is locally asymptotically stable when R 0 < 1 at the disease-free case. For R 0 ≤ 1 , we show the global asymptotical stability of the model. We consider the infected cases in Saudi Arabia and determine the parameters of the model. We show that for the real cases, the basic reproduction is R 0 ≈ 1 . 7372 . We further extend the Caputo model into piecewise stochastic fractional differential equations and discuss the procedure for its numerical simulation. Numerical simulations for the Caputo case and piecewise models are shown in detail.