A conformable mathematical model for alcohol consumption in Spain

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.

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

Advances in Mechanical Engineering ◽

10.1177/1687814017690069 ◽

2017 ◽

Vol 9 (2) ◽

pp. 168781401769006 ◽

Cited By ~ 20

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.

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Modeling, analysis and numerical solution to malaria fractional model with temporary immunity and relapse

Advances in Difference Equations ◽

10.1186/s13662-021-03532-4 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Attiq ul Rehman ◽

Ram Singh ◽

Thabet Abdeljawad ◽

Eric Okyere ◽

Liliana Guran

Keyword(s):

Fractional Order ◽

Equilibrium Points ◽

Order Derivative ◽

Fractional Order Derivative ◽

Modeling Analysis ◽

Proposed Model ◽

Adomian Decomposition ◽

Uniqueness Of The Solution ◽

The Stability ◽

Temporary Immunity

AbstractThe present paper deals with a fractional-order mathematical epidemic model of malaria transmission accompanied by temporary immunity and relapse. The model is revised by using Caputo fractional operator for the index of memory. We also recommend the utilization of temporary immunity and the possibility of relapse. The theory of locally bounded and Lipschitz is employed to inspect the existence and uniqueness of the solution of the malaria model. It is shown that temporary immunity has a great effect on the dynamical transmission of host and vector populations. The stability analysis of these equilibrium points for fractional-order derivative α and basic reproduction number $\mathcal{R}_{0}$ R 0 is discussed. The model will exhibit a Hopf-type bifurcation. The two control variables are introduced in this model to decrease the number of populations. Mandatory conditions for the control problem are produced. Two types of numerical method via Laplace Adomian decomposition and Runge–Kutta of fourth order for simulating the proposed model with fractional-order derivative are presented. To validate the mathematical results, numerical simulations, sensitivity analysis, convergence analysis, and other important studies are given. The paper is finished with some conclusions and discussion.

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

Complexity ◽

10.1155/2021/1904067 ◽

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.

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A new mathematical model for Zika virus transmission

Advances in Difference Equations ◽

10.1186/s13662-020-03044-7 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 2

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.

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

Axioms ◽

10.3390/axioms10030228 ◽

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.

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Study of a Fractional-Order Epidemic Model of Childhood Diseases

Journal of Function Spaces ◽

10.1155/2020/5895310 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8 ◽

Cited By ~ 2

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.

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A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

Journal of Function Spaces ◽

10.1155/2021/1273405 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Hakimeh Mohammadi ◽

Mohammed K. A. Kaabar ◽

Jehad Alzabut ◽

A. George Maria Selvam ◽

Shahram Rezapour

Keyword(s):

Fractional Derivative ◽

Fractional Order ◽

Fixed Point Theory ◽

Equilibrium Points ◽

Hemorrhagic Fever ◽

Order Derivative ◽

Common Disease ◽

Fractional Order Derivative ◽

Crimean Congo Hemorrhagic Fever ◽

Caputo Fractional Order Derivative

Crimean-Congo hemorrhagic fever is a common disease between humans and animals that is transmitted to humans through infected ticks, contact with infected animals, and infected humans. In this paper, we present a boxed model for the transmission of Crimean-Congo fever virus. With the help of the fixed-point theory, our proposed system model is investigated in detail to prove its unique solution. Given that the Caputo fractional-order derivative preserves the system’s historical memory, we use this fractional derivative in our modeling. The equilibrium points of the proposed system and their stability conditions are determined. Using the Euler method for the Caputo fractional-order derivative, we calculate the approximate solutions of the fractional system, and then, we present a numerical simulation for the transmission of Crimean-Congo hemorrhagic fever.

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GENERALIZED THEORY OF MAGNETO-THERMO-VISCOELASTIC SPHERICAL CAVITY PROBLEM UNDER FRACTIONAL ORDER DERIVATIVE: STATE SPACE APPROACH

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.86 ◽

2020 ◽

Vol 9 (11) ◽

pp. 9769-9780

Author(s):

S.G. Khavale ◽

K.R. Gaikwad

Keyword(s):

State Space ◽

Fractional Order ◽

Order Derivative ◽

Laplace Inversion ◽

State Space Approach ◽

Spherical Region ◽

Fractional Order Derivative ◽

Numerical Laplace Inversion ◽

Mathcad Software ◽

Space Approach

This paper is dealing the modified Ohm's law with the temperature gradient of generalized theory of magneto-thermo-viscoelastic for a thermally, isotropic and electrically infinite material with a spherical region using fractional order derivative. The general solution obtained from Laplace transform, numerical Laplace inversion and state space approach. The temperature, displacement and stresses are obtained and represented graphically with the help of Mathcad software.

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Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

Advances in Difference Equations ◽

10.1186/s13662-020-03087-w ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Choonkil Park ◽

R. I. Nuruddeen ◽

Khalid K. Ali ◽

Lawal Muhammad ◽

M. S. Osman ◽

...

Keyword(s):

Fractional Derivative ◽

Fractional Order ◽

Mathematical Physics ◽

Order Derivative ◽

Conformable Fractional Derivative ◽

Fractional Order Derivative ◽

De Vries ◽

Fifth Order ◽

2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

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