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 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 Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769006 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Maysaa Al Qurashi ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Logistic Equation ◽  
Iterative Technique ◽  
Uniqueness Of The Solution

In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo–Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.

scholarly journals On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Areej S. S. Alharbi ◽  
Hamed H. Alsulami ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Admissible Function ◽  
Point Theory ◽  
Contractive Condition ◽  
Simulation Function ◽  
The Given ◽  
Admissible Functions

We investigate the existence and uniqueness of certain operators which form a new contractive condition via the combining of the notions of admissible function and simulation function contained in the context of completeb-metric spaces. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

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.

Dynamical Analysis of Fractional Order Model for Computer Virus Propagation with Kill Signals

2020 ◽  
Vol 21 (3-4) ◽  
pp. 239-247 ◽  
Author(s):  
Necati Özdemir ◽  
Sümeyra Uçar ◽  
Beyza Billur İskender Eroğlu
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Computer Network ◽  
Computer Virus ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Order Model ◽  
Virus Propagation ◽  
Fractional Order Model ◽  
Matlab Program

AbstractThe kill signals are alert about possible viruses that infect computer network to decrease the danger of virus propagation. In this work, we focus on a fractional-order SEIR-KS model in the sense of Caputo derivative to analyze the effects of kill signal nodes on the virus propagation. For this purpose, we first prove the existence and uniqueness of the model and give qualitative analysis. Then, we obtain the numerical solution of the model by using the Adams–Bashforth–Moulton algorithm. Finally, the effects of model parameters are demonstrated with graphics drawn by MATLAB program.

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 Study of a Fractional-Order Epidemic Model of Childhood Diseases

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Aman Ullah ◽  
Thabet Abdeljawad ◽  
Shabir Ahmad ◽  
Kamal Shah
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Childhood Diseases ◽  
Proposed Model ◽  
Adomian Decomposition ◽  
Uniqueness Of The Solution

In this article, we discuss the existence and uniqueness of the solution of the fractional-order epidemic model of childhood diseases by using fixed point theory. The technique of natural transform coupled with the Adomian decomposition is used to find the solution of the proposed model. At the end of the article, the model is demonstrated with appropriate numerical and graphical description.

scholarly journals Oscillatory and complex behaviour of Caputo-Fabrizio fractional order HIV-1 infection model

2021 ◽  
Vol 7 (3) ◽  
pp. 4778-4792
Author(s):  
Shabir Ahmad ◽  
◽  
Aman Ullah ◽  
Mohammad Partohaghighi ◽  
Sayed Saifullah ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Picard Iteration ◽  
Infection Model ◽  
Theory Approach ◽  
Complex Behaviour ◽  
Hiv 1

<abstract><p>HIV-1 infection is a dangerous diseases like Cancer, AIDS, etc. Many mathematical models have been introduced in the literature, which are investigated with different approaches. In this article, we generalize the HIV-1 model through nonsingular fractional operator. The non-integer mathematical model of HIV-1 infection under the Caputo-Fabrizio derivative is presented in this paper. The concept of Picard-Lindelof and fixed-point theory are used to address the existence of a unique solution to the HIV-1 model under the suggested operator. Also, the stability of the suggested model is proved through the Picard iteration and fixed point theory approach. The model's approximate solution is constructed through three steps Adams-Bashforth numerical method. Numerical simulations are provided for different values of fractional-order to study the complex dynamics of the model. Lastly, we provide the oscillatory and chaotic behavior of the proposed model for various fractional orders.</p></abstract>

scholarly journals A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Aslam ◽  
Rashid Murtaza ◽  
Thabet Abdeljawad ◽  
Ghaus ur Rahman ◽  
Aziz Khan ◽  
...  
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Lagrange Interpolation ◽  
Infection Model ◽  
Order Model ◽  
Aids Epidemic ◽  
Fractional Order Model ◽  
Fixed Point Technique ◽  
The Stability ◽  
Hiv Aids

AbstractIn this article, we study a fractional order HIV/AIDS infection model with ABC-fractional derivative. The model is based on four classes of a population. The study includes the existence and uniqueness of solution, the stability analysis, and simulations. We utilize the fixed point technique for the existence and uniqueness analysis. The stability of the fractional order model is derived with the help of existing literature for the Hyers–Ulam stability. For the numerical computations, the Lagrange interpolation is utilized, and the simulations are obtained for specific parameters. The results are closer to the classical results for different orders.

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