scholarly journals Mathematical Modeling and Forecasting of COVID-19 in Saudi Arabia under Fractal-Fractional Derivative in Caputo Sense with Power-Law

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 228
Author(s):  
Mdi Begum Jeelani ◽  
Abeer S. Alnahdi ◽  
Mohammed S. Abdo ◽  
Mansour A. Abdulwasaa ◽  
Kamal Shah ◽  
...  
Keyword(s):  
Saudi Arabia ◽  
Fractional Order ◽  
Power Law ◽  
Reproduction Number ◽  
Fixed Point Theory ◽  
Fractal Dimensions ◽  
Real Data ◽  
Point Theory ◽  
Modeling And Forecasting ◽  
Uniqueness Of The Solution

This manuscript is devoted to investigating a fractional-order mathematical model of COVID-19. The corresponding derivative is taken in Caputo sense with power-law of fractional order μ and fractal dimension χ. We give some detailed analysis on the existence and uniqueness of the solution to the proposed problem. Furthermore, some results regarding basic reproduction number and stability are given. For the proposed theoretical analysis, we use fixed point theory while for numerical analysis fractional Adams–Bashforth iterative techniques are utilized. Using our numerical scheme is verified by using some real values of the parameters to plot the approximate solution to the considered model. Graphical presentations corresponding to different values of fractional order and fractal dimensions are given. Moreover, we provide some information regarding the real data of Saudi Arabia from 1 March 2020 till 22 April 2021, then calculated the fatality rates by utilizing the SPSS, Eviews and Expert Modeler procedure. We also built forecasts of infection for the period 23 April 2021 to 30 May 2021, with 95% confidence.

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.

A conformable mathematical model for alcohol consumption in Spain

2019 ◽  
Vol 12 (05) ◽  
pp. 1950057 ◽  
Author(s):  
Aqsa Nazir ◽  
Naveed Ahmed ◽  
Umar Khan ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Alcohol Consumption ◽  
Fractional Order ◽  
Fixed Point Theory ◽  
Sharp Decrease ◽  
Variational Iteration Method ◽  
Point Theory ◽  
Order Derivative ◽  
Fractional Order Derivative ◽  
Analytical Technique ◽  
Uniqueness Of The Solution

A study on the conformable model of alcohol consumption in Spain has been presented. For the proposed model, the existence as well as the uniqueness of the solution has been discussed with the help of fixed-point theory. An analytical technique, Variational Iteration Method (VIM), has been used to obtain the solution to the governing system of differential equations. With the help of suitable plots, the role of fractional order derivative has been highlighted. For decreasing values of fractional order derivative, decrease in the number of non-consumers and non-risk consumers has been observed. By increasing the value of fractional order derivative, a sharp decrease can be seen in the compartment of risk-consumers. The agreement between the current study and the already existing studies, with ordinary derivatives, has also been pointed out.

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 On modeling of coronavirus-19 disease under Mittag-Leffler power law

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Samia Bushnaq ◽  
Kamal Shah ◽  
Hussam Alrabaiah
Keyword(s):  
Numerical Simulation ◽  
Fixed Point ◽  
Fractional Order ◽  
Power Law ◽  
Fixed Point Theory ◽  
Numerical Technique ◽  
Approximate Solutions ◽  
Point Theory ◽  
New Model

Abstract This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as $(\mathcal{ABC})$ ( ABC ) . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

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.

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 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 A ROBUST COMPUTATIONAL DYNAMICS OF FRACTIONAL-ORDER SMOKING MODEL WITH RELAPSE HABIT

Fractals ◽  
2021 ◽  
Author(s):  
ANWAR ZEB ◽  
SUNIL KUMAR ◽  
TAREQ SAEED
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Computational Dynamics ◽  
The Social ◽  
Banach Contraction ◽  
Bad Breath ◽  
Predictor Corrector ◽  
Good Agreement

The social habit of smoking has affected the whole world in a social manner. It is the main cause of diseases like cancers, asthma, bad breath, etc., and a source of spreading of infectious diseases like COVID-19. This work is related to an existing smoking model with relapse habit converted in fractional order. First, formulation of fractional-order smoking model is presented and then the dynamics of proposed problem is analyzed. Fixed-point theory via Banach contraction and Schauder theorems is used to derive the existence and uniqueness of the model. At last, the adaptive predictor–corrector algorithm and Runge–Kutta fourth-order (RK4) strategy are used to perform simulation. To bolster the validity of the theoretical results, a set of numerical simulations are performed. A good agreement between hypothetical and numerical results is demonstrated via numerical simulations using MATLAB software.

scholarly journals A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 122
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Isnani Darti
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Power Law ◽  
Existence And Uniqueness ◽  
Dynamical Analysis ◽  
Prey Interaction ◽  
Uniqueness Of The Solution ◽  
Over Exploitation ◽  
Caputo Fractional Order Derivative

The harvesting management is developed to protect the biological resources from over-exploitation such as harvesting and trapping. In this article, we consider a predator–prey interaction that follows the fractional-order Rosenzweig–MacArthur model where the predator is harvested obeying a threshold harvesting policy (THP). The THP is applied to maintain the existence of the population in the prey–predator mechanism. We first consider the Rosenzweig–MacArthur model using the Caputo fractional-order derivative (that is, the operator with the power-law kernel) and perform some dynamical analysis such as the existence and uniqueness, non-negativity, boundedness, local stability, global stability, and the existence of Hopf bifurcation. We then reconsider the same model involving the Atangana–Baleanu fractional derivative with the Mittag–Leffler kernel in the Caputo sense (ABC). The existence and uniqueness of the solution of the model with ABC operator are established. We also explore the dynamics of the model with both fractional derivative operators numerically and confirm the theoretical findings. In particular, it is shown that models with both Caputo operator and ABC operator undergo a Hopf bifurcation that can be controlled by the conversion rate of consumed prey into the predator birth rate or by the order of fractional derivative. However, the bifurcation point of the model with the Caputo operator is different from that of the model with the ABC operator.

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].

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