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 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.

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 Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alberto Cabada ◽  
Om Kalthoum Wanassi
Keyword(s):  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Part ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Exhaustive Study ◽  
The Banach Contraction Principle

Abstract This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive study of the sign of the related Green’s function is carried out. Under suitable assumptions on the asymptotic behavior of the nonlinear part of the equation at zero and at infinity, and by application of the fixed point theory of compact operators defined in suitable cones, it is proved that there exists at least one solution of the considered problem. Moreover, the method of lower and upper solutions is developed and the existence of solutions is deduced by a combination of both techniques. In particular cases, the Banach contraction principle is used to ensure the uniqueness of solutions.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

Positive solutions and stability of fuzzy Atangana–Baleanu variable fractional differential equation model for a novel coronavirus (COVID-19)

2021 ◽  
pp. 2150059
Author(s):  
Pratibha Verma ◽  
Manoj Kumar
Keyword(s):  
Positive Solution ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Fuzzy Variable ◽  
Point Theory ◽  
Equation Model ◽  
Theory Approach ◽  
Fractional Differential ◽  
Novel Coronavirus ◽  
Rassias Stability

This work provides a new fuzzy variable fractional COVID-19 model and uses a variable fractional operator, namely, the fuzzy variable Atangana–Baleanu fractional derivatives in the Caputo sense. Next, we explore the proposed fuzzy variable fractional COVID-19 model using the fixed point theory approach and determine the solution’s existence and uniqueness conditions. We choose an appropriate mapping and with the help of the upper/lower solutions method. We prove the existence of a positive solution for the proposed fuzzy variable fractional COVID-19 model and also obtain the result on the existence of a unique positive solution. Moreover, we discuss the generalized Hyers–Ulam stability and generalized Hyers–Ulam–Rassias stability. Further, we investigate the results on maximum and minimum solutions for the fuzzy variable fractional COVID-19 model.

scholarly journals Application of topological degree method in quantitative behavior of fractional differential equations

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 421-432
Author(s):  
Rahman ur ◽  
Saeed Ahmad ◽  
Fazal Haq
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Research Article ◽  
Fractional Differential ◽  
Topological Degree Method

In the present manuscript we incorporate fractional order Caputo derivative to study a class of non-integer order differential equation. For existence and uniqueness of solution some results from fixed point theory is on our disposal. The method used for exploring these existence results is topological degree method and some auxiliary conditions are developed for stability analysis. For further elaboration an illustrative example is provided in the last part of the research article.

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.

scholarly journals Existence Theory and Novel Iterative Method for Dynamical System of Infectious Diseases

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Gauhar Ali ◽  
Ghazala Nazir ◽  
Kamal Shah ◽  
Yongjin Li
Keyword(s):  
Dynamical System ◽  
Existence And Uniqueness ◽  
Integral Transform ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Qualitative Theory ◽  
Existence Theory ◽  
Uniqueness Of The Solution ◽  
Respective Theory

This manuscript is devoted to investigate qualitative theory of existence and uniqueness of the solution to a dynamical system of an infectious disease known as measles. For the respective theory, we utilize fixed point theory to construct sufficient conditions for existence and uniqueness of the solution. Some results corresponding to Hyers–Ulam stability are also investigated. Furthermore, some semianalytical results are computed for the considered system by using integral transform due to the Laplace and decomposition technique of Adomian. The obtained results are presented by graphs also.

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 Existence of Solution to a Second-Order Boundary Value Problem via Noncompactness Measures

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wen-Xue Zhou ◽  
Jigen Peng
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Dirichlet Boundary ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Of Solution ◽  
Dirichlet Boundary Value Problem ◽  
Condensing Mapping

The existence and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.

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