Novel adaptive control approach to fractal fractional order deforestation model and its impact on soil erosion.

Deforestation exerts profound ramifications on soil quality and biodiversity, thereby exerting substantial economic repercussions. The depletion of organic matter and structural integrity of soil following tree removal for agricultural purposes underscores the severity of this issue. In elucidating the soil pollution stemming from deforestation, this research employs a sophisticated five-compartment SDIFR model integrating fractal dimension and fractional order dynamics.

A plethora of novel solitary wave solutions related to van der Waals equation: a comparative study.

In this article, we explore exact solitary wave solutions to the van der Waals equation which is crucial for numerous applications involving a variety of physical occurrences. This system is used to define the behavior of real gases taking into consideration finite size of molecules and also has some applications in industry for granular materials. The model is studied under the effect of fractional derivatives by employing two different definitions: , and M-truncated.

Coherent manipulation of giant birefringent Goos-Hänchen shifts by compton scattering using chiral atomic medium.

A four level chiral medium is considered to analyze and investigate theoretically the reflection/transmission coefficients of right circularly polarized (RCP) beam and left circularly polarized (LCP) beam as well as their corresponding GH-shifts under the effect of compton scattering. Density matrix formalism is used for calculation of electric and magnetic probe fields coherence. The polarization and magnetization are calculated from probes coherence terms in the chiral medium.

Analysis of multi-wave solitary solutions of (2+1)-dimensional coupled system of Boiti-Leon-Pempinelli.

This work examines the (2+1)-dimensional Boiti-Leon-Pempinelli model, which finds its use in hydrodynamics. This model explains how water waves vary over time in hydrodynamics. We provide new explicit solutions to the generalized (2+1)-dimensional Boiti-Leon-Pempinelli equation by applying the Sardar sub-equation technique.

Analysis of some dynamical systems by combination of two different methods.

In this study, we introduce a novel iterative method combined with the Elzaki transformation to address a system of partial differential equations involving the Caputo derivative. The Elzaki transformation, known for its effectiveness in solving differential equations, is incorporated into the proposed iterative approach to enhance its efficiency. The system of partial differential equations under consideration is characterized by the presence of Caputo derivatives, which capture fractional order dynamics.

Cholera disease dynamics with vaccination control using delay differential equation.

The COVID-19 pandemic came with many setbacks, be it to a country's economy or the global missions of organizations like WHO, UNICEF or GTFCC. One of the setbacks is the rise in cholera cases in developing countries due to the lack of cholera vaccination. This model suggested a solution by introducing another public intervention, such as adding Chlorine to water bodies and vaccination.

Mathematical modelling and control approach for sustainable ecosystems in mitigating the impact of pollutants on aquatic species in rivers.

This paper focuses on the urgent issue of minimising the impact of pollutants on aquatic life in river ecosystems. Our innovative approach involves the integration of mathematical modelling and strategic control methods to counteract the negative consequences of industrial and agricultural activities. The model, developed in a one-dimensional context, captures the complex dynamics of species population and pollutant concentration.

Optimum study of fractional polio model with exponential decay kernel.

This study introduces a fractional order model to investigate the dynamics of polio disease spread, focusing on its significance, unique results, and conclusions. We emphasize the importance of understanding polio transmission dynamics and propose a novel approach using a fractional order model with an exponential decay kernel. Through rigorous analysis, including existence and stability assessment applying the Caputo Fabrizio fractional operator, we derive key insights into the disease dynamics.

Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator.

COVID-19 is linked to diabetes, increasing the likelihood and severity of outcomes due to hyperglycemia, immune system impairment, vascular problems, and comorbidities like hypertension, obesity, and cardiovascular disease, which can lead to catastrophic outcomes. The study presents a novel COVID-19 management approach for diabetic patients using a fractal fractional operator and Mittag-Leffler kernel. It uses the Lipschitz criterion and linear growth to identify the solution singularity and analyzes the global derivative impact, confirming unique solutions and demonstrating the bounded nature of the proposed system.

Heat transfer innovation of engine oil conveying SWCNTs-MWCNTs-TiO nanoparticles embedded in a porous stretching cylinder.

The influence of boundary layer flow of heat transfer analysis on hybrid nanofluid across an extended cylinder is the main focus of the current research. In addition, the impressions of magnetohydrodynamic, porous medium and thermal radiation are part of this investigation. Arrogate similarity variables are employed to transform the governing modelled partial differential equations into a couple of highly nonlinear ordinary differential equations.

Numerical study of diffusive fish farm system under time noise.

In the current study, the fish farm model perturbed with time white noise is numerically examined. This model contains fish and mussel populations with external food supplied. The main aim of this work is to develop time-efficient numerical schemes for such models that preserve the dynamical properties.

Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures.

To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model.

Neuro-computing solution for Lorenz differential equations through artificial neural networks integrated with PSO-NNA hybrid meta-heuristic algorithms: a comparative study.

In this article, examine the performance of a physics informed neural networks (PINN) intelligent approach for predicting the solution of non-linear Lorenz differential equations. The main focus resides in the realm of leveraging unsupervised machine learning for the prediction of the Lorenz differential equation associated particle swarm optimization (PSO) hybridization with the neural networks algorithm (NNA) as ANN-PSO-NNA. In particular embark on a comprehensive comparative analysis employing the Lorenz differential equation for proposed approach as test case.

Investigating double-diffusive natural convection in a sloped dual-layered homogenous porous-fluid square cavity.

This article investigates natural convection with double-diffusive properties numerically in a vertical bi-layered square enclosure. The cavity has two parts: one part is an isotropic and homogeneous porous along the wall, and an adjacent part is an aqueous fluid. Adiabatic, impermeable horizontal walls and constant and uniform temperatures and concentrations on other walls are maintained.

Analytical investigation of Carreau fluid flow through a non-circular conduit with wavy wall.

Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions.

Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study.

The current research presents a novel technique for numerically solving the one-dimensional advection-diffusion equation. This approach utilizes subdivision scheme based collocation method to interpolate the space dimension along with the finite difference method for the time derivative. The proposed technique is examined on a variety of problems and the obtained results are presented both quantitatively in tables and visually in figures.