scholarly journals Epidemic Model of Leptospirosis Containing Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
S. F. Saddiq ◽  
Saeed Islam ◽  
Ilyas Khan ◽  
Dennis Ling Chuan Ching
Keyword(s):  
Approximate Solution ◽  
Positive Solution ◽  
Fractional Order ◽  
Epidemic Model ◽  
Differential Transform Method ◽  
Unique Positive Solution ◽  
Transform Method ◽  
Differential Transform ◽  
Generalized Differential ◽  
Order Four

We study an epidemic model of leptospirosis in fractional order numerically. The multistep generalized differential transform method is applied to find the accurate approximate solution of the epidemic model of leptospirosis disease in fractional order. A unique positive solution for the epidemic model in fractional order is presented. For the integer case derivative, the approximate solution of MGDTM is compared with the Runge-Kutta order four scheme. The numerical results are presented for the justification purpose.

scholarly journals Solution of HIV and Malaria Coinfection Model Using Msgdtm

2015 ◽  
Vol 7 (4) ◽  
pp. 181
Author(s):  
Bonyah Ebenezer ◽  
Kwasi Awuah-Werekoh ◽  
Joseph Acquah
Keyword(s):  
Approximate Solution ◽  
Fractional Order ◽  
Epidemic Model ◽  
Unique Positive Solution ◽  
Transform Method ◽  
Order Form ◽  
Differential Transform ◽  
Infection Disease ◽  
Generalized Differential ◽  
Order Four

<p>In this paper, we investigate an epidemic model of HIV and Malaria co-infection using fractional order Calculus (FOC). The multistep generalized differential transform method (MSGDTM) is employed to obtain an accurate approximate solution to the epidemic model of HIV and Malaria co-infection disease in fractional order. A unique positive solution for HIV and Malaria co-infection is presented in fractional order form. For the integer case derivatives, the approximate solution of MSGDTM and the Runge–Kutta–order four scheme are compared. Numerical results are produced for the justification for this method.</p>

scholarly journals Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shaher Momani ◽  
Asad Freihat ◽  
Mohammed AL-Smadi
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Generalized Differential

The multistep generalized differential transform method is applied to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model. The algorithm is illustrated by studying the dynamics of three coupled chaotic FHN neurons equations with different gap junctions under external electrical stimulation. The fractional derivatives are described in the Caputo sense. Furthermore, we present figurative comparisons between the proposed scheme and the classical fourth-order Runge-Kutta method to demonstrate the accuracy and applicability of this method. The graphical results reveal that only few terms are required to deduce the approximate solutions which are found to be accurate and efficient.

Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order

2021 ◽  
Vol 8 (3) ◽  
pp. 537-548
Author(s):  
S. E. Fadugba ◽  
◽  
F. Ali ◽  
A. B. Abubakar ◽  
◽  
...  
Keyword(s):  
Power Series ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Epidemic Model ◽  
Differential Transform Method ◽  
Host Community ◽  
Convergent Power Series ◽  
Transform Method ◽  
Differential Transform ◽  
Reduced Differential Transform Method

This paper proposes the Caputo Fractional Reduced Differential Transform Method (CFRDTM) for Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model with fractional order in a host community. CFRDTM is the combination of the Caputo Fractional Derivative (CFD) and the well-known Reduced Differential Transform Method (RDTM). CFRDTM demonstrates feasible progress and efficiency of operation. The properties of the model were analyzed and investigated. The fractional SEIR epidemic model has been solved via CFRDTM successfully. Hence, CFRDTM provides the solutions of the model in the form of a convergent power series with easily computable components without any restrictive assumptions.

Comparison of Numerical Methods of the SEIR Epidemic Model of Fractional Order

2014 ◽  
Vol 69 (1-2) ◽  
pp. 81-89 ◽  
Author(s):  
Anwar Zeb ◽  
Madad Khan ◽  
Gul Zaman ◽  
Shaher Momani ◽  
Vedat Suat Ertürk
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Nonnegative Solution ◽  
Incidence Rates ◽  
Kutta Method ◽  
Transform Method ◽  
Seir Model ◽  
Runge Kutta Method ◽  
Differential Transform ◽  
Generalized Differential

In this paper, we consider the SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model by taking into account both standard and bilinear incidence rates of fractional order. First, the nonnegative solution of the SEIR model of fractional order is presented. Then, the multi-step generalized differential transform method (MSGDTM) is employed to compute an approximation to the solution of the model of fractional order. Finally, the obtained results are compared with those obtained by the fourth-order Runge-Kutta method and non-standard finite difference (NSFD) method in the integer case.

scholarly journals Application of Multistep Generalized Differential Transform Method for the Solutions of the Fractional-Order Chua's System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Asad Freihat ◽  
Shaher Momani
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Dynamical Behavior ◽  
Nonlinear Behavior ◽  
Nonlinear Problems ◽  
Differential Transform Method ◽  
Effective Dimension ◽  
Transform Method ◽  
Differential Transform ◽  
Generalized Differential

We numerically investigate the dynamical behavior of the fractional-order Chua's system. By utilizing the multistep generalized differential transform method (MSGDTM), we find that the fractional-order Chua's system with “effective dimension” less than three can exhibit chaos as well as other nonlinear behavior. Numerical results are presented graphically and reveal that the multistep generalized differential transform method is an effective and convenient method to solve similar nonlinear problems in fractional calculus.

scholarly journals "Approximate solution for the two-dimensional Volterra-Integro differential equation of fractional order by using Generalized Deferential Transform method "

2018 ◽  
Vol 5 (2) ◽  
pp. 1-9
Author(s):  
Mohammed G. S. AL-Safi ◽  
Wurood R. Abd AL- Hussein
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Fractional Order ◽  
Two Dimensional ◽  
Transform Method ◽  
Integro Differential Equation ◽  
Numerical Example ◽  
Differential Transform ◽  
Generalized Differential

"In this work, an efficient generalized differential transform method (GDTM) is proposed for solving the twodimensional Volterra-Integro differential equation (2-DVIDE) of fractional order. The results of the proposed method are compared with exact solution, a numerical example is considered for testing the accuracy and validity of this method."

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