scholarly journals Epidemiological analysis of fractional order COVID-19 model with Mittag-Leffler kernel

2022 ◽  
Vol 7 (1) ◽  
pp. 756-783
Author(s):  
Muhammad Farman ◽  
◽  
Ali Akgül ◽  
Kottakkaran Sooppy Nisar ◽  
Dilshad Ahmad ◽  
...  
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Control Strategies ◽  
Point Theory ◽  
Fractional Operators ◽  
Order Model ◽  
Epidemiological Analysis ◽  
Fractional Order Model ◽  
Sumudu Transform

<abstract> <p>This paper derived fractional derivatives with Atangana-Baleanu, Atangana-Toufik scheme and fractal fractional Atangana-Baleanu sense for the COVID-19 model. These are advanced techniques that provide effective results to analyze the COVID-19 outbreak. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model COVID-19 model. We also proved the property of boundedness and positivity for the fractional-order model. The Atangana-Baleanu technique and Fractal fractional operator are used with the Sumudu transform to find reliable results for fractional order COVID-19 Model. The generalized Mittag-Leffler law is also used to construct the solution with the different fractional operators. Numerical simulations are performed for the developed scheme in the range of fractional order values to explain the effects of COVID-19 at different fractional values and justify the theoretical outcomes, which will be helpful to understand the outbreak of COVID-19 and for control strategies.</p> </abstract>

scholarly journals Investigation of COVID-19 Mathematical  Model Under Fractional Order Derivative

2021 ◽  
Author(s):  
Kamal Shah ◽  
Muhammad Arfan ◽  
Meshal Shutaywi ◽  
Wejdan Deebani ◽  
Dumitru Balaneau
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Theory Approach ◽  
Order Model ◽  
Fractional Order Model ◽  
Testing Data ◽  
Series Type ◽  
The Given

The given article is devoted to presentation of some results regarding existence and uniqueness of solution to a fractional order model that addressing the effect of immigration on the transmission dynamics of a population model. Further, in view of this investigation the effect of immigration have been checked on transmission of recent pandemic known as Corona virus Covid-19. The concerned results have been established by using fixed point theory approach. After investigation qualitative analysis of the considered model, by applying Laplace transform along with decomposition method, we have calculated some series type results for the concerned model. The unknown quantities of each equation have been decomposed into small quantities to calculate each small quantity very easily for the series solution by adding first few terms of the said quantities. Approximate results of some testing data with different cases are given to illustrate the results.

scholarly journals Numerical solution of a fractal-fractional order chaotic circuit system

2021 ◽  
Vol 67 (5 Sep-Oct) ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Abdon Atangana ◽  
Taseer Muhammad ◽  
Ebraheem Alzahrani
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Research Area ◽  
Fractional Operators ◽  
Chaotic Circuit ◽  
Order Model ◽  
Fractional Order Model ◽  
Chaotic Model ◽  
Important Research Area ◽  
Fractional Orders

The dynamical system has an important research area and due to its wide applications many researchers and scientists working to develop new model and techniques for their solution. We present in this work the dynamics of a chaotic model in the presence of newly introduced fractal-fractional operators. The model is formulated initially in ordinary differential equations and then we utilize the fractal-fractional (FF) in power law, exponential and Mittag-Leffler to generalize the model. For each fractal-fractional order model, we briefly study its numerical solution via the numerical algorithm. We present some graphical results with arbitrary order of fractal and fractional orders, and present that these operators provide different chaotic attractors for different fractal and fractional order values. The graphical results demonstrate the effectiveness of the fractal-fractional operators.

scholarly journals ANALYSIS OF FRACTAL–FRACTIONAL MALARIA TRANSMISSION MODEL

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040041 ◽  
Author(s):  
J. F. GÓMEZ-AGUILAR ◽  
T. CÓRDOVA-FRAGA ◽  
THABET ABDELJAWAD ◽  
AZIZ KHAN ◽  
HASIB KHAN
Keyword(s):  
Malaria Transmission ◽  
Exponential Decay ◽  
Power Law ◽  
Fixed Point Theory ◽  
Control Strategies ◽  
Point Theory ◽  
Transmission Model ◽  
Fractional Operators ◽  
Uniqueness And Existence ◽  
Exponential Decay Law

In this paper, the malaria transmission (MT) model under control strategies is considered using the Liouville–Caputo fractional order (FO) derivatives with exponential decay law and power-law. For the solutions we are using an iterative technique involving Laplace transform. We examined the uniqueness and existence (UE) of the solutions by applying the fixed-point theory. Also, fractal–fractional operators that include power-law and exponential decay law are considered. Numerical results of the MT model are obtained for the particular values of the FO derivatives [Formula: see text] and [Formula: see text].

A fractional-order model of HIV infection: Numerical solution and comparisons with data of patients

2014 ◽  
Vol 07 (04) ◽  
pp. 1450036 ◽  
Author(s):  
A. A. M. Arafa ◽  
S. Z. Rida ◽  
M. Khalil
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Real Data ◽  
Euler Method ◽  
Order Model ◽  
Fractional Order Model ◽  
Plasma Virus Load ◽  
Hiv 1

In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus (HIV-1) infection is presented. Numerical solutions are obtained using a generalized Euler method (GEM) to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These comparisons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model.

scholarly journals A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Hakimeh Mohammadi
Keyword(s):  
Fractional Order ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Point Theory ◽  
Euler Method ◽  
Transmission Model ◽  
Order Model ◽  
Influenza Transmission ◽  
The Stability ◽  
Disease Free

Abstract We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. In the numerical section, we present a simulation to examine the system, in which we calculate equilibrium points of the system and examine the behavior of the resulting functions at the equilibrium points. By calculating the results of the model for different fractional order, we examine the effect of the derivative order on the behavior of the resulting functions and obtained numerical values. We also calculate the results of the integer-order model and examine their differences with the results of the fractional-order model.

Numerical investigation of fractional model of Phytoplankton–Toxic Phytoplankton–Zooplankton system with convergence analysis

2021 ◽  
Author(s):  
Ved Prakash Dubey ◽  
Jagdev Singh ◽  
Ahmed M. Alshehri ◽  
Sarvesh Dubey ◽  
Devendra Kumar
Keyword(s):  
Fractional Order ◽  
Computational Methods ◽  
Fixed Point Theory ◽  
Time Derivative ◽  
Point Theory ◽  
Power Series Method ◽  
Transform Method ◽  
Toxic Phytoplankton ◽  
Wide Range ◽  
Sumudu Transform

In this paper, a fractional order model of the phytoplankton–toxic phytoplankton–zooplankton system with Caputo fractional derivative is investigated via three computational methods, namely, residual power series method (RPSM), homotopy perturbation Sumudu transform method (HPSTM) and the homotopy analysis Sumudu transform method (HASTM). This model is constituted by three components: phytoplankton, toxic phytoplankton and zooplankton. Phytoplankton species are self-feeding members of the plankton community and play a very significant role in ecosystems. A wide range of sea creatures get food through phytoplankton. This paper focuses on the implementation of the three above-mentioned computational methods for a nonlinear time-fractional phytoplankton–toxic phytoplankton–zooplankton (PTPZ) model with a perception to study the dynamics of a model. This study shows that the solutions obtained by employing the suggested computational methods are in good agreement with each other. The computational procedures reveal that the HASTM solution generates a more general solution as compared to RPSM and HPSTM and incorporates their results as a special case. The numerical results presented in the form of graphs authenticate the accuracy of computational schemes. Hence, the implemented methods are very appropriate and relevant to handle nonlinear fractional models. In addition, the effect of variation of fractional order of a time derivative and time [Formula: see text] on populations of phytoplankton, toxic–phytoplankton and zooplankton has also been studied through graphical presentations. Moreover, the uniqueness and convergence analyses of HASTM solution have also been discussed in view of the Banach fixed-point theory.

scholarly journals Fractional order COVID-19 model with transmission rout infected through environment

2022 ◽  
Vol 7 (4) ◽  
pp. 5156-5174
Author(s):  
Shao-Wen Yao ◽  
◽  
Muhammad Farman ◽  
Maryam Amin ◽  
Mustafa Inc ◽  
...  
Keyword(s):  
Fractional Order ◽  
Iterative Scheme ◽  
Fractional Operator ◽  
Order Model ◽  
Fractional Order Model ◽  
Sumudu Transform ◽  
Visual Depiction ◽  
Model Formation ◽  
Sensitive Parameters ◽  
The Given

<abstract><p>In this paper, we study a fractional order COVID-19 model using different techniques and analysis. The sumudu transform is applied with the environment as a route of infection in society to the proposed fractional-order model. It plays a significant part in issues of medical and engineering as well as its analysis in community. Initially, we present the model formation and its sensitivity analysis. Further, the uniqueness and stability analysis has been made for COVID-19 also used the iterative scheme with fixed point theorem. After using the Adams-Moulton rule to support our results, we examine some results using the fractal fractional operator. Demonstrate the numerical simulations to prove the efficiency of the given techniques. We illustrate the visual depiction of sensitive parameters that reveal the decrease and triumph over the virus within the network. We can reduce the virus by the appropriate recognition of the individuals in community of Saudi Arabia.</p></abstract>

scholarly journals Extended Fractional-Order Jeffreys Model of Viscoelastic Hydraulic Cylinder

2021 ◽  
Author(s):  
Michael Ruderman
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Hydraulic Cylinder ◽  
Inertial Forces ◽  
Response Functions ◽  
Order Model ◽  
Fractional Order Model ◽  
Jeffreys Model ◽  
Hydraulic Cylinders ◽  
Parameter Constraints

Abstract Novel modeling approach for viscoelastic hydraulic cylinders with negligible inertial forces is proposed based on the extended fractional-order Jeffreys model. Analysis and physical reasoning for the parameter constraints and order of the fractional derivatives are provided. The comparison between the measured and computed frequency response functions and time domain transient response argue in favor of the proposed four-parameters fractional-order model.

Sign in / Sign up

Export Citation Format

Share Document