Fractional Model Research Articles

Fractional derivative modeling of heat transfer and fluid flow around a contracting permeable infinite cylinder: Computational study

Understanding the complex interplay between the contracting behavior of the cylinder and the fluid flow dynamics has implications for the design of porous structures for heat exchange and filtration systems. In this study, we investigate the dynamics and thermal behavior of fluid flow past a contracting permeable infinite cylinder. First, we developed a mathematical model based on the Navier–Stokes equations to describe the fluid dynamics around the contracting permeable infinite cylinder. A new simple well-behaved definition of fractional derivative called conformal fractional derivative introduced by authors Khalil et al., (2014) is employed to generalize the PDE’s of momentum and energy. The similarity transformation technique is utilized to transform the proposed mathematical problem into a non-linear ODE’s. Then, we utilized IPS technique to numerically solve the governing equations and obtain detailed insights into the flow patterns and thermal characteristics. We observed significant changes in the flow velocity and temperature distribution as the cylinder contracted, highlighting the intricate thermal behavior of the system. Additionally, the changes in the fraction order was found to have a notable impact on the overall flow patterns and heat transfer processes.

Fractional non-Fourier modeling of laser drilling process

In this paper, a novel fractional non-Fourier model is employed to simulate the laser drilling process, addressing limitations inherent in classical heat conduction equations, including the well-known heat equation paradox associated with infinite heat propagation velocity. This model approach combines spatial approximation via the Meshless Local Petrov-Galerkin method with temporal approximation using the Grünwald-Letnikov finite difference scheme. The study assesses the impact of employing fractional orders, both constant and variable over time, on numerical results, and validates the model using experimental data.

Computational framework for analyzing fractional biochemical reaction model

Computational framework for analyzing fractional biochemical reaction model

Fractional order cancer model infection in human with CD8+ T cells and anti-PD-L1 therapy: simulations and control strategy

In order to comprehend the dynamics of disease propagation within a society, mathematical formulations are essential. The purpose of this work is to investigate the diagnosis and treatment of lung cancer in persons with weakened immune systems by introducing cytokines (IL2&IL12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ IL_{2} \\& IL_{12}$$\\end{document}) and anti-PD-L1 inhibitors. To find the stable position of a recently built system TCDIL2IL12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$IL_{2} IL_{12}$$\\end{document}Z, a qualitative and quantitative analysis are taken under sensitive parameters. Reliable bounded findings are ensured by examining the generated system’s boundedness, positivity, uniqueness, and local stability analysis, which are the crucial characteristics of epidemic models. The positive solutions with linear growth are shown to be verified by the global derivative, and the rate of impact across every sub-compartment is determined using Lipschitz criteria. Using Lyapunov functions with first derivative, the system’s global stability is examined in order to evaluate the combined effects of cytokines and anti-PD-L1 inhibitors on people with weakened immune systems. Reliability is achieved by employing the Mittag-Leffler kernel in conjunction with a fractal-fractional operator because FFO provide continuous monitoring of lung cancer in multidimensional way. The symptomatic and asymptomatic effects of lung cancer sickness are investigated using simulations in order to validate the relationship between anti-PD-L1 inhibitors, cytokines, and the immune system. Also, identify the actual state of lung cancer control with early diagnosis and therapy by introducing cytokines and anti-PD-L1 inhibitors, which aid in the patients’ production of anti-cancer cells. Investigating the transmission of illness and creating control methods based on our validated results will both benefit from this kind of research.

The creep behaviors of red sandstone in northern Yunnan and its fractional order damage modelling considering relaxation time effect

The creep behaviors of red sandstone in northern Yunnan and its fractional order damage modelling considering relaxation time effect

Fractional analysis of unsteady magnetohydrodynamics Jeffrey flow over an infinite vertical plate in the presence of Hall current

The impact of Hall current on the multiphase thermal transfer of an incompressible electrically conductive Jeffrey flow over an infinitely vertical plate when heat absorption and chemical reaction are present has been examined. Partial differential equations have been used to describe the process, accounting for heat and mass transfer effects. This study uses extended Fourier's and Fick's laws together with the recently announced constant proportional Caputo (CPC) fractional operator. The fractional model is converted into a nondimensional form by applying some appropriate quantities. The nondimensional produced fractional model for momentum, heat, and diffusion equations based on the CPC fractional operator has been calculated semi‐analytically by applying the Laplace method. The Mathcad 15 software to sketch the graphs for several factors, like the Grashof number, mass Grashof number, Schmidt number, Prandtl number, Hall, and magnetic field parameters, is used to describe the velocity profile. Additionally, a graphical explanation is provided for the influence of the appeared parameters, particularly the effect of the fractional parameters. It is concluded that the result of the fluid model developed by the generalized constitutive relations is more accurate and generalized than the results of the artificially contracted fractional model. A fractional derivative is therefore the ideal option to achieve controlled concentration, temperature, and velocity. The current study is immediately relevant to geophysical, cosmically fluid dynamics, medical, biological, and any other processes that are significantly enhanced by a low gas density and a high magnetic field.

Analytical and fractional model for power transmission of lossy transmission line

ABSTRACT A lossy transmission line can draw current from DC source if DC voltage is applied to constant resistance. This manuscript proposes a fractional modeling of lossy transmission line based on the partial differential equations by employing Kirchoff’s current and voltage laws via Fourier analysis. The governing equation of lossy transmission line is fractionalized by means of modern fractional differential operators. The optimal solution of voltage is investigated by means of Fourier sine and Laplace transforms subject to the imposed conditions. The solutions of voltage over the transmission line have been investigated in terms of exponential and gamma functions. The comparative analysis of voltage over the transmission line through Caputo-Fabrizio and Atangana-Baleanu fractional operators has been presented for line losses on the basis of conductance, resistance and inductance for power transmission.

Analysis of fractional Euler-Bernoulli bending beams using Green’s function method

This paper deals with the effect of fractional order on the fractional Euler-Bernoulli beams model. This model is based on the elastic curve that can be approximated using tangent lines and the osculating circle. We introduce a general form of the fractional Green’s function for the highest-order term 1<α≤2, which gives a unique solution for the geometrical fractional bending beams with an inhomogeneous fractional differential equation. The analytical closed-form responses were obtained by inverse problem technique and integration over Green’s function kernel. The theory and properties of fractional Green’s function method are described by generalizing classical theory to the initial and two-point fractional boundary value problems. Static analysis of the numerical examples, such as determinate and indeterminate beams with typical loads and beam property boundary conditions, are presented and discussed. The results were verified using the direct integration method. The fractional conventional ratio indicates the beam's deformation deviation from its classical state. The analysis results reveal that changing the fractional parameter significantly impacts the deflection behavior of flexural beams due to the beam’s characteristics and the fractional order. The behavior of the fractional beam is identical to the classical state when the fractional parameter is an integer number.

Methylene Blue Adsorption Kinetics Investigation by Coconut Shell Activated Carbon Adsorbent Using Fractional Power, Avrami and Bangham Models

Methylene blue is not easily biodegradable, and its persistence in water can contribute to long-term contamination if not properly treated. Numerous adsorption kinetic study successes were achieved utilizing activated carbons of coconut shell, especially the Pseudo-First and Pseudo-Second order models with little/no regards to the unique behavior described by the Avrami, Bangham and the Fractional Power kinetic models. The parameters in those models are determined to describe the sorption mechanism. Avrami model fitting results suggests a complex adsorption process, which does not follow the first-order kinetic. Obtained results show that the Fractional Power model best described the Coconut Shell-Activated Carbon Methylene blue bio-sorption process at constant adsorption capacity of 15937.8 mg/g. Findings show that Bangham kinetic model does not fit the experimental data for Methylene blue sorption from aqueous solution. Methylene blue exposure issues like gastrointestinal discomfort, skin and eye irritation, and imbalances in the populations of various species in aquatic ecosystems due to impacts on their growth, reproduction and survival, may be solved using a very effective adsorbent, such as the Coconut Shell -Activated Carbon used here.

Mathematical analysis of a novel fractional order vaccination model for Tuberculosis incorporating susceptible class with underlying ailment

ABSTRACT Tuberculosis (TB) is a communicable, airborne infection caused by the bacillus Mycobacterium tuberculosis. Pulmonary tuberculosis (PTB) is the most common presentation, although infection can spread anywhere to cause extra-pulmonary tuberculosis (EPTB). In this paper, a novel fractional order mathematical model is designed for the transmission dynamics of tuberculosis. Uninfected vulnerable individuals are categorized into the following: susceptible with underline ailment and susceptible without underline ailment. The research seeks to qualitatively and quantitatively analyze the proposed model and suggests comprehensive intervention measures for the control of tuberculosis among individuals with underline ailment. Some of the major highlights from the numerical investigation points out that TB vaccination is key to reducing the spread of TB among individuals with underline ailment. Furthermore, efforts to step down the spread of TB through awareness campaigns could significantly reduce the burden of the disease among individuals with co-morbidity.

Prediction of servo industry development in China by an optimized reverse Hausdorff fractional discrete grey power model

Prediction of servo industry development in China by an optimized reverse Hausdorff fractional discrete grey power model

Generalization of Bernoulli polynomials to find optimal solution of fractional hematopoietic stem cells model

The study introduces a fractional mathematical model in the Caputo sense for hematopoietic stem cell-based therapy, utilizing generalized Bernoulli polynomials (GBPs) and operational matrices to solve a system of nonlinear equations. The significance of the study lies in the potential therapeutic applications of hematopoietic stem cells (HSCs), particularly in the context of HIV infection treatment, and the innovative use of GBPs and Lagrange multipliers in solving the fractional hematopoietic stem cells model (FHSCM). The aim of the study is to introduce an optimization algorithm for approximating the solution of the FHSCM using GBPs and Lagrange multipliers and to provide a comprehensive exploration of the mathematical techniques employed in this context. The research methodology involves formulating operational matrices for fractional derivatives of GBPs, conducting a convergence analysis of the proposed method, and demonstrating the accuracy of the method through numerical simulations. The major conclusion is the successful introduction of GBPs in the context of the FHSCM, featuring innovative control parameters and a novel optimization technique. The study also highlights the significance of the proposed method in providing accurate solutions for the FHSCM, thus contributing to the field of mathematical modeling in biological and medical research.

Using torsional wave elastography to evaluate spring pot parameters in skin tumor mimicking phantoms

Estimating the tissue parameters of skin tumors is crucial for diagnosis and effective therapy in dermatology and related fields. However, identifying the most sensitive biomarkers require an optimal rheological model for simulating skin behavior this remains an ongoing research endeavor. Additionally, the multi-layered structure of the skin introduces further complexity to this task. In order to surmount these challenges, an inverse problem methodology, in conjunction with signal analysis techniques, is being employed. In this study, a fractional rheological model is presented to enhance the precision of skin tissue parameter estimation from the acquired signal from torsional wave elastography technique (TWE) on skin tumor-mimicking phantoms for lab validation and the estimation of the thickness of the cancerous layer. An exhaustive analysis of the spring-pot model (SP) solved by the finite difference time domain (FDTD) is conducted. The results of experiments performed using a TWE probe designed and prototyped in the laboratory were validated against ultrafast imaging carried out by the Verasonics Research System. Twelve tissue-mimicking phantoms, which precisely simulated the characteristics of skin tissue, were prepared for our experimental setting. The experimental data from these bi-layer phantoms were measured using a TWE probe, and the parameters of the skin tissue were estimated using inverse problem-solving. The agreement between the two datasets was evaluated by comparing the experimental data obtained from the TWE technique with simulated data from the SP- FDTD model using Pearson correlation, dynamic time warping (DTW), and time-frequency representation. Our findings show that the SP-FDTD model and TWE are capable of determining the mechanical properties of both layers in a bilayer phantom, using a single signal and an inverse problem approach. The ultrafast imaging and the validation of TWE results further demonstrate the robustness and reliability of our technology for a realistic range of phantoms. This fusion of the SP-FDTD model and TWE, as well as inverse problem-solving methods has the potential to have a considerable impact on diagnoses and treatments in dermatology and related fields.

Fractional modeling of unsteady flow of Jeffrey fluid using active and passive control strategies

The current work is focused on the analysis of heat and mass transfer in a magnetohydrodynamics Jeffrey nanofluid flows across a vertical plate because of these possible uses. Free convection, magnetic effect, and thermo-diffusion properties are all applied to the flow considered here. The modeling also takes into account the passive and active control of the Jeffrey nanofluid. The constant proportional Caputo fractional operator which was recently introduced is used in this work together with generalized Fick’s and Fourier’s law. Using suitable nondimensional variables, ordinary differential equations are obtained from the modeling equations, and the Laplace transform method is used to solve these modeled equations. The concentration and temperature profiles are rising functions of the fractional and thermophoresis parameters, and they drop more quickly as the values of the Schmidt, Prandtl, and Nb (Brownian motion parameters) rise. The constant proportional Caputo (CPC) fractional derivative is the best choice for achieving more stable concentration, temperature, and velocity than conventional fields. Raising the values of α will increase the rate of heat transfer and skin friction coefficient. Additionally, as compared to the classical model, the constant proportional Caputo derivative model shows more decay nature. Consequently, compared to the classical model, the constant proportional Caputo differential model has a superior memory function.

Effect of soil conditioners based on geomimetic materials on plant growth in degraded soils: Poly(acrylic acid)/bentonite

Geomimetic materials (GEOMI) are composite materials based on polymer and clays, able to imitate structural and functional properties of soils, including their structure, cationic exchange capability (CEC), water uptake capability (WUC), pH buffering ability, immobilizing of substances, among other. Because they can be used to develop of fertilizer slow-release systems, they have been identified as a novel approach to advance toward a most sustainable agriculture. The aim of this work was to study the effect of GEOMI on the plant growth in degraded soils. For this, GEOMI-1.0 was synthesized using poly(acrylic acid) as model of humic substances and bentonite modified with trichlorovinylsilane as mineral fraction model. Materials were characterized by different techniques. GEOMI-1.0 showed a hybrid, homogeneous, and amorphous structure. In addition, it was thermally stable at below ⁓200 °C with a Tg about 49.3 °C, showed a high WUC (⁓1384 g of water per 100 g of material). Likewise, it was verified that GEOMI-1.0 can decreases the pH values and increases the CEC of degraded soils depending on the added amount of geomaterial; but also, the electric conductivity values showed no dependence on the added amount of GEOMI-1.0. By correlation analysis, an exponential dependence of CEC was observed respect to pH changes, the relative amount added of GEOMI-1.0 and the initial CEC. Finally, using Brachiaria Brizantha cv. Marandú as plant model, the increase in the biomass content of roots and leaves, and the number of germinated seeds, were observed when GEOMI-1.0 was used for restoration of in-lab degraded soils.

Fractional neutron point kinetics model for reactivity transients of the NuScale and comparison with the classical kinetics approach

In this work, the behavior of the neutron and natural circulation parameters for Reactivity Transients in the PWR reactor called NuScale are analyzed through the novel system equations. It model includes non-integer and ordinary order differentials coupling the neutron point kinetic with the thermos-hydraulic core of the reactor. Transient processes of increase and decrease of the feed flow and the coolant inlet temperature are analyzed to identify the feedback of the thermohydraulic effects with the neutron phenomena in a non-integer order scheme. In the results, it is observed that for short times the power and reactivity have the same behavior with the classical model and the non-integer order model for all values of the anomalous diffusion coefficient simulated. However, for long times of simulation, there is more reactivity and less power, in contrast to the classical model, when reducing the value of the anomalous diffusion coefficient these counter-intuitive effects are increased. Additionally, a delay is observed between the change in reactivity and power. In conclusion, it is observed that sub-diffusive processes are relevant when there are slow changes in reactivity, which can be analyzed through the Fractional Order Neutron Density Equation.

Drivers of overseas labour migration, migration intensity, and destination choice among farming households in Nepal

ABSTRACT In recent years, overseas labour migration has become a lifeline for many households in Nepal. Using survey data from 465 randomly selected households and 227 overseas labour migrants, this paper examines the factors influencing overseas labour migration and migration intensity in farming households by employing a generalised two-part fractional regression model, and migrants’ destination choice by using the probit model. We find that a higher proportion of educated members in the household, along with household’s credit access, indebtedness, and contacts with manpower agencies significantly increase the likelihood of overseas labour migration and migration intensity in the households, whereas the presence of employed members in the household, larger farms, irrigation access, and higher asset index significantly lower such likelihood. We find a lower likelihood of migration to Malaysia and the Middle East countries among individuals with employed household members and a higher asset index, while those connected to manpower agencies are more likely to choose these countries as destinations. Our findings emphasise the significance of creating and providing decent economic opportunities, including strengthening the agriculture sector, to address the existing surge in overseas labour migration from farming households in Nepal.

A fractional mathematical model for vaccinated humans with the impairment of Monkeypox transmission

A fractional mathematical model for vaccinated humans with the impairment of Monkeypox transmission

Performance Analysis of Fully Intuitionistic Fuzzy Multi-Objective Multi-Item Solid Fractional Transportation Model

An investigation is conducted in this paper into a performance analysis of fully intuitionistic fuzzy multi-objective multi-item solid fractional transport model (FIF-MMSFTM). It is to be anticipated that the parameters of the conveyance model will be imprecise by virtue of numerous uncontrollable factors. The model under consideration incorporates intuitionistic fuzzy (IF) quantities of shipments, costs and profit coefficients, supplies, demands, and transport. The FIF-MMSFTM that has been devised is transformed into a linear form through a series of operations. The accuracy function and ordering relations of IF sets are then used to reduce the linearized model to a concise multi-objective multi-item solid transportation model (MMSTM). Furthermore, an examination is conducted on several theorems that illustrate the correlation between the FIF-MMSFTM and its corresponding crisp model, which is founded upon linear, hyperbolic, and parabolic membership functions. A numerical example was furnished to showcase the efficacy and feasibility of the suggested methodology. The numerical data acquired indicates that the linear, hyperbolic, and parabolic models require fewer computational resources to achieve the optimal solution. The parabolic model has the greatest number of iterations, in contrast to the hyperbolic model which has the fewest. Additionally, the elapsed run time for the three models is a negligible amount of time: 0.2, 0.15, and 1.37 s, respectively. In conclusion, suggestions for future research are provided.

Global stability and modeling with a non-singular kernel for fractional order heroin epidemic model: Insights from different population studies

There has been a worldwide epidemic of heroin that has affected people, families, societies, and cultures across the world. Now, the heroin epidemic has transitioned from heroin abuse to the overuse of synthetic narcotics, which are widely accessible and inexpensively produced. In this work, a novel mathematical approach is applied to investigate the dynamics of the heroin epidemic model and its harmful effect on society with different population data. A heroin model has been constructed with the importance of a non-singular kernel in the sense of a generalized Mittag-Leffler kernel. The well-posedness of the proposed model is proven via fixed-point theory. To examine the heroin model, two equilibrium states have been determined. These equilibrium states are proven to be locally and globally asymptotically stable. To analyze the behavior of heroin, a basic reproduction number and sensitivity analysis are used to determine the impact of different parameters mathematically as well as through simulations. To find the approximate solution, we implement the Toufik–Atangana numerical method at different fractional order values. The sensitivity of the heroin model is carried out, and 3-D graphs show the significance of the parameter involved in the model. Finally, the numerical outcomes are presented with different values of fractional parameters.