scholarly journals A Fractional Order Hepatitis C Mathematical Model with Mittag-Leffler Kernel

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Hashim M. Alshehri ◽  
Aziz Khan
Keyword(s):  
Hepatitis C ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Polynomial Interpolation ◽  
Numerical Study ◽  
Classical Model ◽  
Ulam Stability ◽  
Lagrange Polynomial ◽  
Spread Model ◽  
Order Extension

In this paper, a mathematical fractional order Hepatitis C virus (HCV) spread model is presented for an analytical and numerical study. The model is a fractional order extension of the classical model. The paper includes the existence, singularity, Hyers-Ulam stability, and numerical solutions. Our numerical results are based on the Lagrange polynomial interpolation. We observe that the model of fractional order has the same behavior of the solutions as the integer order existing model.

scholarly journals Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 641
Author(s):  
Wang Huang ◽  
Jianjun Yang ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Pihua Wen
Keyword(s):  
Finite Element Method ◽  
Numerical Solutions ◽  
Shape Function ◽  
Polynomial Interpolation ◽  
Finite Domain ◽  
Mapping Technique ◽  
Lagrange Polynomial ◽  
Block Method ◽  
Nonlinear Characteristics ◽  
Typical Material

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

Highly accurate technique for studying some chaotic models described by ABC-fractional differential equations of variable-order

2020 ◽  
pp. 2150018
Author(s):  
M. M. Khader ◽  
Ibrahim Al-Dayel
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Polynomial Interpolation ◽  
Numerical Technique ◽  
Variable Order ◽  
Lagrange Polynomial ◽  
Efficient Tool ◽  
Fractional Differential ◽  
The Given

The propose of this paper is to introduce and investigate a highly accurate technique for solving the fractional Logistic and Ricatti differential equations of variable-order. We consider these models with the most common nonsingular Atangana–Baleanu–Caputo (ABC) fractional derivative which depends on the Mittag–Leffler kernel. The proposed numerical technique is based upon the fundamental theorem of the fractional calculus as well as the Lagrange polynomial interpolation. We satisfy the efficiency and the accuracy of the given procedure; and study the effect of the variation of the fractional-order [Formula: see text] on the behavior of the solutions due to the presence of ABC-operator by evaluating the solution with different values of [Formula: see text]. The results show that the given procedure is an easy and efficient tool to investigate the solution for such models. We compare the numerical solutions with the exact solution, thereby showing excellent agreement which we have found by applying the ABC-derivatives. We observe the chaotic solutions with some fractional-variable-order functions.

scholarly journals Fractional Order Forced Convection Carbon Nanotube Nanofluid Flow Passing Over a Thin Needle

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 312 ◽  
Author(s):  
Taza Gul ◽  
Muhammad Khan ◽  
Waqas Noman ◽  
Ilyas Khan ◽  
Tawfeeq Abdullah Alkanhal ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Forced Convection ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Classical Model ◽  
Single Wall Carbon Nanotubes ◽  
Physical Parameters ◽  
Suitable Model ◽  
Layer Flow ◽  
The Impact

In the fields of fluid dynamics and mechanical engineering, most nanofluids are generally not linear in character, and the fractional order model is the most suitable model for representing such phenomena rather than other traditional approaches. The forced convection fractional order boundary layer flow comprising single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs) with variable wall temperatures passing over a needle was examined. The numerical solutions for the similarity equations were obtained for the integer and fractional values by applying the Adams-type predictor corrector method. A comparison of the SWCNTs and MWCNTs for the classical and fractional schemes was investigated. The classical and fractional order impact of the physical parameters such as skin fraction and Nusselt number are presented physically and numerically. It was observed that the impact of the physical parameters over the momentum and thermal boundary layers in the classical model were limited; however, while utilizing the fractional model, the impact of the parameters varied at different intervals.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

scholarly journals A fractional order epidemic model for the simulation of outbreaks of Ebola

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Safdar Ali
Keyword(s):  
Numerical Solution ◽  
Root Mean Square ◽  
Fractional Order ◽  
Relative Error ◽  
Numerical Solutions ◽  
Real Data ◽  
Mean Square ◽  
Order Model ◽  
The Real ◽  
Fractional Orders

AbstractThe Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number $R_{0}$ R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo–Mainardi–Moretti–Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error $g(U^{*})=0.4146$ g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is $g(U^{*})=0.2744$ g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 787
Author(s):  
Olaniyi Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Complex Nature ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Effective Contact ◽  
Proposed Model ◽  
Fractional Models

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

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