scholarly journals Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Fazal Haq ◽  
Muhammad Shahzad ◽  
Shakoor Muhammad ◽  
Hafiz Abdul Wahab ◽  
Ghaus ur Rahman
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Epidemic Model ◽  
Adomian Decomposition Method ◽  
Classical Case ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Adomian Decomposition ◽  
Fractional Differential

The fractional order Susceptible-Infected-Recovered (SIR) epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.

scholarly journals Solutions of Conformable Fractional-Order SIR Epidemic Model

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Atimad Harir ◽  
Said Malliani ◽  
Lalla Saadia Chandli
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Analytic Solution ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Conformable Fractional Derivative ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Fractional Differential

In this paper, the conformable fractional-order SIR epidemic model are solved by means of an analytic technique for nonlinear problems, namely, the conformable fractional differential transformation method (CFDTM) and variational iteration method (VIM). These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. The VIM is based on conformable fractional derivative and proved. The result revealed that both methods are in agreement and are accurate and efficient for solving systems of OFDE.

scholarly journals A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
José Paulo Carvalho dos Santos ◽  
Lislaine Cristina Cardoso ◽  
Evandro Monteiro ◽  
Nelson H. T. Lemes
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Biological Behavior ◽  
Bovine Babesiosis ◽  
Comparison Theory ◽  
Linearization Theorem ◽  
Fractional Differential

This paper shows that the epidemic model, previously proposed under ordinary differential equation theory, can be generalized to fractional order on a consistent framework of biological behavior. The domain set for the model in which all variables are restricted is established. Moreover, the existence and stability of equilibrium points are studied. We present the proof that endemic equilibrium point when reproduction numberR0>1is locally asymptotically stable. This result is achieved using the linearization theorem for fractional differential equations. The global asymptotic stability of disease-free point, whenR0<1, is also proven by comparison theory for fractional differential equations. The numeric simulations for different scenarios are carried out and data obtained are in good agreement with theoretical results, showing important insight about the use of the fractional coupled differential equations set to model babesiosis disease and tick populations.

scholarly journals An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Moh’d Khier Al-Srihin ◽  
Mohammed Al-Refai
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
New Approach ◽  
Adomian Decomposition ◽  
Fractional Differential

In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.

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