Numerical computation of fractional Lotka-Volterra equation arising in biological systems

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Ramswroop ◽  
Jagdev Singh ◽  
Devendra Kumar
Keyword(s):  
Exact Solution ◽  
Difference Equations ◽  
Volterra Equation ◽  
Auxiliary Function ◽  
Transform Method ◽  
Homotopy Analysis ◽  
Effective Role ◽  
Fractional Differential ◽  
And Control

AbstractIn this paper, we present the homotopy analysis transform method (HATM) to solve fractional Lotka- Volterra equation, which describes the long term servival of species. The HATM solutions, denotes less error compare with their respective exact solution for alpha = 1. In addition to non-proposed techniques, HATMis valid for both small and large parameters, it also provides us with a simpleway to adjust and control the parameter hbar and auxiliary function H(t), which play effective role for convergence solutions of fractional differential-difference equations (FDDEs).

scholarly journals Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1976
Author(s):  
Cyril D. Enyi
Keyword(s):  
Biological Sciences ◽  
Exact Solution ◽  
Population Model ◽  
Two Dimensional ◽  
Transform Method ◽  
One Dimensional ◽  
Analytical Technique ◽  
Extensive Analysis ◽  
Homotopy Analysis ◽  
Fractional Differential

This paper presents an efficacious analytical and numerical method for solution of fractional differential equations. This technique, here in named q-HATM (q-homotopy analysis transform method) is applied to a one-dimensional fractional Fornberg–Whitham model and a two-dimensional fractional population model emanating from biological sciences. The overwhelming agreement of our analytical solution by the q-HATM technique with the exact solution indeed establishes the efficacy of q-HATM to solve the fractional Fornberg–Whitham model and the two-dimensional fractional population model. Furthermore, comparisons by means of extensive analysis using numerics, graphs and error analysis are presented to affirm the preference of q-HATM technique over other methods. A variant of the q-HATM using symmetry can also be considered to solve these problems.

On a new modified fractional analysis of Nagumo equation

2019 ◽  
Vol 12 (03) ◽  
pp. 1950034 ◽  
Author(s):  
Khaled M. Saad ◽  
Si̇nan Deni̇z ◽  
Dumi̇tru Baleanu
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Fractional Derivatives ◽  
Transform Method ◽  
Average Residual ◽  
Homotopy Analysis ◽  
Fractional Analysis ◽  
Nagumo Equation ◽  
Modified Equation

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo–Fabrizio and Atangana–Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called [Formula: see text]-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.

scholarly journals On the Application of Homotopy Analysis Method to Fractional Differential Equations

2021 ◽  
pp. 1-18
Author(s):  
Khalid Suliman Aboodh ◽  
Abu baker Ahmed
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Fractional Differential ◽  
Convergence Control Parameter

In this paper, an attempt has been made to obtain the solution of linear and nonlinear fractional differential equations by applying an analytic technique, namely the homotopy analysis method (HAM). The fractional derivatives are described by Caputo’s sense. By this method, the solution considered as the sum of an infinite series, which converges rapidly to exact solution with the help of the nonzero convergence control parameter ℏ. Some examples are given to show the efficiently and accurate of this method. The solutions obtained by this method has been compared with exact solution. Also our graphical represented of the solutions have been given by using MATLAB software.

Toward a New Algorithm for Nonlinear Fractional Differential Equations

2013 ◽  
Vol 5 (2) ◽  
pp. 222-234
Author(s):  
Fadi Awawdeh ◽  
S. Abbasbandy
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Homotopy Analysis Method ◽  
Analytical Techniques ◽  
Analytic Solutions ◽  
Analysis Method ◽  
Transform Method ◽  
Nonlinear Fractional Differential Equations ◽  
Homotopy Analysis ◽  
Fractional Differential

AbstractThis paper is concerned with the development of an efficient algorithm for the analytic solutions of nonlinear fractional differential equations. The proposed algorithm Laplace homotopy analysis method (LHAM) is a combined form of the Laplace transform method with the homotopy analysis method. The biggest advantage the LHAM has over the existing standard analytical techniques is that it overcomes the difficulty arising in calculating complicated terms. Moreover, the solution procedure is easier, more effective and straightforward. Numerical examples are examined to demonstrate the accuracy and efficiency of the proposed algorithm.

scholarly journals A mathematical analysis of a system of Caputo–Fabrizio fractional differential equations for the anthrax disease model in animals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Sina Etemad ◽  
Hakimeh Mohammadi
Keyword(s):  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Disease Model ◽  
Time Interval ◽  
Transform Method ◽  
Homotopy Analysis ◽  
Sumudu Transform ◽  
Existence Criterion ◽  
Fractional Differential ◽  
The Stability

Abstract We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional $\mathcal {CF}$ CF -system of the anthrax disease model by utilizing the Picard–Lindelof technique. By obtaining the basic reproduction number $\mathcal{R}_{0}$ R 0 of the fractional $\mathcal{CF}$ CF -system we compute two disease-free and endemic equilibrium points and check the asymptotic stability property. Moreover, by applying an iterative approach based on the Sumudu transform we investigate the stability of the fractional $\mathcal{CF}$ CF -system. We obtain approximate series solutions of this system by means of the homotopy analysis transform method, in which we invoke the linear Laplace transform. Finally, after the convergence analysis of the numerical method HATM, we present a numerical simulation of the $\mathcal{CF}$ CF -fractional anthrax disease model and review the dynamical behavior of the solutions of this $\mathcal {CF}$ CF -system during a time interval.

Analytical solutions of some integral fractional differential–difference equations

2019 ◽  
Vol 34 (01) ◽  
pp. 2050009 ◽  
Author(s):  
Jian-Gen Liu ◽  
Xiao-Jun Yang ◽  
Yi-Ying Feng
Keyword(s):  
Invariant Subspace ◽  
Difference Equations ◽  
Analytical Solutions ◽  
Volterra Equation ◽  
Burgers Equation ◽  
Space Time ◽  
Subspace Method ◽  
Lattice Equation ◽  
Fractional Differential

The invariant subspace method (ISM) is a powerful tool for investigating analytical solutions to fractional differential–difference equations (FDDEs). Based on previous work by other people, we apply the ISM to the space-time fractional differential and difference equations, including the cases of the scalar space-time FDDEs and the multi-coupled space-time FDDEs. As a result, we obtain some new analytical solutions to the well-known scalar space-time Lotka–Volterra equation, the space-time fractional generalized Hybrid lattice equation and the space-time fractional Burgers equation as well as two couple space-time FDDEs. Furthermore, some properties of the analytical solutions are illustrated by graphs.

Suppressed, but Not Forgotten

2011 ◽  
Vol 70 (1) ◽  
pp. 5-11 ◽  
Author(s):  
Beat Meier ◽  
Anja König ◽  
Samuel Parak ◽  
Katharina Henke
Keyword(s):  
Memory Trace ◽  
Thought Suppression ◽  
Test Phase ◽  
Indirect Test ◽  
Final Test ◽  
Test Experiment ◽  
And Control ◽  
Cue Words ◽  
The Impact

This study investigates the impact of thought suppression over a 1-week interval. In two experiments with 80 university students each, we used the think/no-think paradigm in which participants initially learn a list of word pairs (cue-target associations). Then they were presented with some of the cue words again and should either respond with the target word or avoid thinking about it. In the final test phase, their memory for the initially learned cue-target pairs was tested. In Experiment 1, type of memory test was manipulated (i.e., direct vs. indirect). In Experiment 2, type of no-think instructions was manipulated (i.e., suppress vs. substitute). Overall, our results showed poorer memory for no-think and control items compared to think items across all experiments and conditions. Critically, however, more no-think than control items were remembered after the 1-week interval in the direct, but not in the indirect test (Experiment 1) and with thought suppression, but not thought substitution instructions (Experiment 2). We suggest that during thought suppression a brief reactivation of the learned association may lead to reconsolidation of the memory trace and hence to better retrieval of suppressed than control items in the long term.

Strengthening of occupational health promotion by the German Prevention Health Care Act

2019 ◽  
pp. 188-190
Author(s):  
Diana Hart
Keyword(s):  
Public Health ◽  
Health Care ◽  
Health Promotion ◽  
Primary Prevention ◽  
Occupational Health ◽  
Life Expectancy ◽  
Prevention And Control ◽  
Occupational Health Promotion ◽  
And Control

All countries are faced with the problem of the prevention and control of non-communicable diseases (NCD): implement prevention strategies eff ectively, keep up the momentum with long term benefi ts at the individual and the population level, at the same time tackling hea lth inequalities. Th e aff ordability of therapy and care including innovative therapies is going to be one of the key public health priorities in the years to come. Germany has taken in the prevention and control of NCDs. Germany’s health system has a long history of guaranteeing access to high-quality treatment through universal health care coverage. Th r ough their membership people are entitled to prevention and care services maintaining and restoring their health as well as long term follow-up. Like in many other countries general life expectancy has been increasing steadily in Germany. Currently, the average life expectancy is 83 and 79 years in women and men, respectively. Th e other side of the coin is that population aging is strongly associated with a growing burden of disease from NCDs. Already over 70 percent of all deaths in Germany are caused by four disease entities: cardiovascular disease, cancer, chronic respiratory disease and diabetes. Th ese diseases all share four common risk factors: smoking, alcohol abuse, lack of physical activity and overweight. At the same time, more and more people become long term survivors of disease due to improved therapy and care. Th e German Government and public health decision makers are aware of the need for action and have responded by initiating and implementing a wide spectrum of activities. One instrument by strengthening primary prevention is the Prevention Health Care Act. Its overarching aim is to prevent NCDs before they can manifest themselves by strengthening primary prevention and health promotion in diff erent sett ings. One of the main emphasis of the Prevention Health Care Act is the occupational health promotion at the workplace.

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