scholarly journals On analysis of a nonlinear fractional system for social media addiction involving Atangana–Baleanu–Caputo derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jutarat Kongson ◽  
Weerawat Sudsutad ◽  
Chatthai Thaiprayoon ◽  
Jehad Alzabut ◽  
Chutarat Tearnbucha
Keyword(s):  
Social Media ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Point Theory ◽  
Social Media Addiction ◽  
Proposed Model ◽  
Reproduction Numbers ◽  
The Stability ◽  
Predictor Corrector ◽  
Fractional Orders

AbstractA mathematical model for the dynamic systems of $\mathbb{SMA}$ SMA involving the $\mathbb{ABC}$ ABC -fractional derivative is considered in this manuscript. We examine the basic reproduction number and analyze the stability of the equilibrium points. We prove the theoretical results of the existence and Ulam’s stability of the solutions for the proposed model using fixed point theory and nonlinear analytic techniques. Using the Adams type predictor–corrector rule for the $\mathbb{ABC}$ ABC -fractional integral operator, a numerical scheme is devised for obtaining the approximate solution of the proposed model. Different numerical plots corresponding to various fractional orders are presented. In addition, we demonstrate a numerical simulation for the transmission of social media addiction in two cases with the basic reproduction numbers greater than and less than one.

An efficient numerical simulation and mathematical modeling for the prevention of tuberculosis

2021 ◽  
Author(s):  
Zain Ul Abadin Zafar ◽  
Samina Younas ◽  
Sumera Zaib ◽  
Cemil Tunç
Keyword(s):  
Fixed Point Theory ◽  
Dynamical Behavior ◽  
Point Theory ◽  
Model Parameters ◽  
Fractional Operator ◽  
Significant Preference ◽  
Relevant Model ◽  
Clinical Associations ◽  
Predictor Corrector ◽  
Fractional Orders

The main purpose of this research is to use a fractional-mathematical model including Atangana–Baleanu derivatives to explore the clinical associations and dynamical behavior of the tuberculosis. Herein, we used a lately introduced fractional operator having Mittag-Leffler kernel. The existence and inimitability problems to the relevant model were examined through the fixed-point theory. To verify the significance of the arbitrary fractional-order derivative, numerical outcomes were explored from the biological and mathematical viewpoints using the values of model parameters. The graphical simulations show the comparison of the predictor–corrector method (PCM) and Caputo method (CM) for different fractional orders and the results indicated the significant preference of PCM over CM.

FRACTIONAL ORDER ANALYSIS OF HBV AND HCV CO-INFECTION UNDER ABC DERIVATIVE

Fractals ◽  
2021 ◽  
Author(s):  
HUSSAM ALRABAIAH ◽  
MATI UR RAHMAN ◽  
IBRAHIM MAHARIQ ◽  
SAMIA BUSHNAQ ◽  
MUHAMMAD ARFAN
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Approximate Solution ◽  
Fractional Order ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Comparative Result ◽  
Order Analysis ◽  
The Stability ◽  
Fractional Orders

In this paper, we consider a fractional mathematical model describing the co-infection of HBV and HCV under the non-singular Mittag-Leffler derivative. We also investigate the qualitative analysis for at least one solution and a unique solution by applying the approach fixed point theory. For an approximate solution, the technique of the iterative fractional order Adams–Bashforth scheme has been implemented. The simulation for the proposed scheme has been drawn at various fractional order values lying between (0,1) and integer-order of 1 via using Matlab. All the compartments have shown convergence and stability with time. A detailed comparative result has been given by the different fractional orders, which showed that the stability was achieved more rapidly at low orders.

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.

scholarly journals Study of HIV Disease and Its Association with Immune Cells under Nonsingular and Nonlocal Fractal-Fractional Operator

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Shabir Ahmad ◽  
Aman Ullah ◽  
Ali Akgül ◽  
Manuel De la Sen
Keyword(s):  
Fractional Order ◽  
Primary Infection ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Hiv Model ◽  
Proposed Model ◽  
Lethal Infection ◽  
Uniqueness Of The Solution ◽  
Fractional Orders

HIV, like many other infections, is a severe and lethal infection. Fractal-fractional operators are frequently used in modeling numerous physical processes in the current decade. These operators provide better dynamics of a mathematical model because these are the generalization of integer and fractional-order operators. This paper aims to study the dynamics of the HIV model during primary infection by fractal-fractional Atangana–Baleanu (AB) operators. The sufficient conditions for the existence and uniqueness of the solution of the proposed model under the AB operator are derived via fixed point theory. The numerical scheme is presented by using the Adams–Bashforth method. Numerical results are demonstrated for different fractal and fractional orders to see the effect of fractional order and fractal dimension on the dynamics of HIV and CD4+ T-cells during primary infection.

scholarly journals A new mathematical model for Zika virus transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Hakimeh Mohammadi ◽  
Amin Jajarmi
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Zika Virus ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Virus Transmission ◽  
Point Theory ◽  
Euler Method ◽  
Order Derivative ◽  
The Stability

Abstract We present a new mathematical model for the transmission of Zika virus between humans as well as between humans and mosquitoes. In this way, we use the fractional-order Caputo derivative. The region of the feasibility of system and equilibrium points are calculated, and the stability of equilibrium point is investigated. We prove the existence of a unique solution for the model by using the fixed point theory. By using the fractional Euler method, we get an approximate solution to the model. Numerical results are presented to investigate the effect of fractional derivative on the behavior of functions and also to compare the integer-order derivative and fractional-order derivative results.

scholarly journals Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zareen A. Khan ◽  
Mati ur Rahman ◽  
Kamal Shah
Keyword(s):  
Fixed Point ◽  
Fractal Dimension ◽  
Incidence Rate ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Harmonic Mean ◽  
The Stability ◽  
Fractional Orders

This manuscript investigates fractal-fractional order smoking models with relapse and harmonic mean type incidence rate under the Caputo derivative. We derive the existence and unique results about the solution for the considered model via fixed point theory. For the stability of the considered system, Ulam-Hyers (UH) approach is used. We compute the numerical solution by using fractional Adams-Bashforth method. For the simulation of the model, we consider different values of fractional order δ and fractal dimension θ by using some real values of the parameters. The proposed scheme is used to simulate the available data for some smoking community including potential, light, and quit smokers. Various graphical presentations are given to understand the dynamics of the model at various fractional orders.

scholarly journals A computational study of transmission dynamics for dengue fever with a fractional approach

2021 ◽  
Author(s):  
Sunil Kumar ◽  
R. P. Chauhan ◽  
Jagdev Singh ◽  
Devendra Kumar
Keyword(s):  
Dengue Fever ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Research Study ◽  
Fixed Point Theory ◽  
Computational Study ◽  
Disease Model ◽  
Point Theory ◽  
Proposed Model ◽  
Predictor Corrector

Fractional derivatives are considered as influential weapon in terms of analysis of infectious disease. The research study in fractional calculus with formulation of new definitions and mathematical tools have a great impact in sector of community health by controlling some fatal diseases. In this article, a generalized version of Caputo derivative which represented as (${}^\mathrm{C}\mathrm{D}_0^{\beta,\sigma}$), is used in alternate modelling of dengue fever disease model. We discuss the existence and uniqueness of solution of model by using fixed point theory. After that, an adaptive predictor-corrector numerical scheme is used to obtain the imminent solution of the proposed model.

scholarly journals SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Hakimeh Mohammadi ◽  
Mohammad Esmael Samei
Keyword(s):  
Epidemic Model ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Real Data ◽  
Point Theory ◽  
Euler Method ◽  
Simulation Based ◽  
The World ◽  
Feasibility Region ◽  
The Stability

Abstract We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibrium points is investigated. We prove the existence of a unique solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. To predict the transmission of COVID-19 in Iran and in the world, we provide a numerical simulation based on real data.

scholarly journals Model Matematika SIR Sebagai Solusi Kecanduan Penggunaan Media Sosial

2020 ◽  
Vol 3 (2) ◽  
pp. 126
Author(s):  
Syafruddin Side ◽  
Wahidah Sanusi ◽  
Nur Khaerati Rustan
Keyword(s):  
Social Media ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sir Model ◽  
Primary Data ◽  
Type Model ◽  
Social Media Addiction ◽  
Reproduction Numbers ◽  
Simulation Results ◽  
Use Of Social Media

Penelitian ini bertujuan untuk membangun model SIR (Susceptible – Infected – Recovered) sebagai solusi kecanduan penggunaan media sosial dengan asumsi bahwa mahasiswa yang sembuh dari kecanduan media sosial karena memiliki kontrol diri tinggi. Model ini dibagi menjadi tiga kelas yaitu kelas mahasiswa yang berpotensi menggunakan media sosial, kelas mahasiswa yang kecanduan media sosial, dan kelas mahasiswa yang memiliki kontrol diri tinggi. Data yang digunakan adalah data primer yang diperoleh dengan membagikan kuesioner kepada 145 mahasiswa Jurusan Matematika FMIPA UNM angkatan 2017, 2018, dan 2019. Hasil data riil model tipe SIR menghasilkan bilangan reproduksi dasar (R0) sebesar  yang berarti bahwa jumlah mahasiswa yang kecanduan penggunaan media sosial akan meningkat dalam kurun waktu tertentu.Kata Kunci: Titik Ekuilibrium, Bilangan Reproduksi Dasar, Media Sosial, Kontrol Diri, Model SIRThis study aims to build the SIR (Susceptible - Infected - Recovered) model as a solution of social media addiction with the assumption that students who recover from addiction of social media because they have high selfcontrol. This model is divided into three classes: namely class of students who have potential to use social media, class of students who are addicted to social media, and class of students who have high selfcontrol. The data used are primary data that was obtained by distributing questionnaires to 145 students of mathematics departement FMIPA UNM class of 2017, 2018, and 2019. The simulation results of the SIR type model produce a basic reproduction number (R0) of 1.451136 which means that the number of students who are addicted to the use of social media will increase in a certain period of time.Keywords: Equilibrium Points, Basic Reproduction Numbers, Social Media, Selfcontrol, SIR Model

scholarly journals On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

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