University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
1
2017
01
01
Numerical analysis of fractional order model of HIV-1 infection of CD4+ T-cells
1
11
EN
Fazal
Haq
Department of Mathematics,
Hazara University Mansehra, Pakistan
fazalhaqphd@gmail.com
Kamal
Shah
Department of Mathematics,
University of Malakand, Chakadara Dir(L),
Khyber Pakhtunkhwa, Pakistan
kamalshah408@gmail.com
Ghaus-UR-
Rahman
Department of Mathematics and Statistics,
University of Swat, Pakistan
r.ghaus@uswat.edu.pk
Muhammad
Shahzad
Department of Mathematics,
Hazara University Mansehra, Pakistan
shahzadmaths@hu.edu.pk
In this article, we present a fractional order HIV-1 infection model of CD4+ T-cell. We analyze the effect of the changing the average number of the viral particle N with initial conditions of the presented model. The Laplace Adomian decomposition method is applying to check the analytical solution of the problem. We obtain the solutions of the fractional order HIV-1 model in the form of infinite series. The concerned series rapidly converges to its exact value. Moreover, we compare our results with the results obtained by Runge-Kutta method in case of integer order derivative.
Infectious diseases models, Fractional Derivatives, Laplace transform , Adomian decomposi- tion method,Analytical solution
http://cmde.tabrizu.ac.ir/article_5825.html
http://cmde.tabrizu.ac.ir/article_5825_f4866fc1855d93e48a17375f970401ef.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
1
2017
01
01
Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets
12
29
EN
Robab
Alikhani
Department of Mathematics,
University of Tabriz, Tabriz, Iran
alikhani@tabrizu.ac.ir
This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of interval H-difference that we will be faced it under weak conditions. The method is illustrated by an examples.
Interval fractional integrodifferential equations,Caputo-Fabrizio fractional derivative,Method of upper or lower solutions,Fixed point in partially ordered sets
http://cmde.tabrizu.ac.ir/article_5832.html
http://cmde.tabrizu.ac.ir/article_5832_a153da52e918984455148c1c2bcc3054.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
1
2017
01
01
New Solutions for Fokker-Plank Equation of Special Stochastic Process via Lie Point Symmetries
30
42
EN
Elham
Dastranj
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
dastranj.e@gmail.com
S. Reza
Hejazi
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
ra.hejazi@gmail.com
In this paper Lie symmetry analysis is applied in order to find new solutions for Fokker Plank equation of Ornstein-Uhlenbeck process. This analysis classifies the solutions format of the Fokker Plank equation by using the Lie algebra of the symmetries of our considered stochastic process.
Financial market,Ornstein-Uhlenbeck,Lie algebra symmetries,Fokker-Plank
http://cmde.tabrizu.ac.ir/article_5860.html
http://cmde.tabrizu.ac.ir/article_5860_0619691dc5e6d56d4bebd5478457bf27.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
1
2017
01
01
Numerical solution of the forced Duffing equations using Legendre multiwavelets
43
55
EN
Ramin
Najafi
Department of Mathematics
Maku Branch, Islamic Azad University,
Maku, Iran
raminnajafi984@gmail.com
Behzad
Nemati Saray
Faculty of Mathematics,
Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
bn.saray@iasbs.ac.ir
A numerical technique based on the collocation method using Legendre multiwavelets are presented for the solution of forced Duffing equation. The operational matrix of integration for Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation to the solution of linear algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Forced Duffing equations,Multiwavelet,Operational matrix of integration,Collocation method
http://cmde.tabrizu.ac.ir/article_5861.html
http://cmde.tabrizu.ac.ir/article_5861_ca3f0ed7de5017b87aa945ff661cf787.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
1
2017
01
01
Sinc operational matrix method for solving the Bagley-Torvik equation
56
66
EN
Mohammad-Reza
Azizi
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
mohamadrezaazizi52@gmail.com
Ali
Khani
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
khani@azaruniv.edu
The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equation to some algebraic equations. It is well known that the sinc procedure converges to the solution at an exponential rate. Numerical examples are included to demonstrate the validity and applicability of the technique.
Bagley-Torvik equation,Sinc functions,Operational matrix,Caputo derivative,Numerical methods
http://cmde.tabrizu.ac.ir/article_5868.html
http://cmde.tabrizu.ac.ir/article_5868_fdcacac6135f0bb82c1b80f8d91e4a6b.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
5
1
2017
01
01
The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications
67
87
EN
Mohammadreza
Ahmadi Darani
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
ahmadi.darani@sci.sku.ac.ir
Abbas
Saadatmandi
Department of Applied Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan, 87317-51167, Iran
saadatmandi@kashanu.ac.ir
In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the solution of a system of algebraic equations. Several numerical examples are given to illustrate the accuracy of our method. The results obtained, are in full agreement with the analytical solutions and numerical results presented by some previous works.
Chebyshev polynomials,orthogonal system,fractional differential equation,fractional-order Chebyshev functions,Operational matrix
http://cmde.tabrizu.ac.ir/article_5902.html
http://cmde.tabrizu.ac.ir/article_5902_97563e2dfae2abcda93be4bd14ba9e1c.pdf