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
Hazara University
fazalhaqphd@gmail.com
Kamal
Shah
University of Malakand
kamalshah408@gmail.com
Ghausur
rahman
University of Swat
r.ghaus@uswat.edu.pk
Muhammad
Shahzad
Hazara University
shahzadmaths@hu.edu.pk
In this article, we present a fractional order HIV-1 infectionmodel of CD4+ T-cell. We analyze the effect of the changing the averagenumber of the viral particle N with initial conditions of the presentedmodel. The Laplace Adomian decomposition method is applying to checkthe analytical solution of the problem. We obtain the solutions of thefractional order HIV-1 model in the form of infinite series. The concernedseries rapidly converges to its exact value. Moreover, we compare ourresults with the results obtained by Runge-Kutta method in case of integerorder 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 Applied Mathematics- Faculty of Mathematical Sciences- University of Tabriz
alikhani@tabrizu.ac.ir
This work is devoted to the study of global solution for initialvalue problem of interval fractional integrodifferential equationsinvolving Caputo-Fabrizio fractional derivative without singularkernel admitting only the existence of a lower solution or an uppersolution. Our method is based on fixed point in partially orderedsets. In this study, we guaranty the existence of special kind ofinterval H-difference that we will be faced it under weakconditions. 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
Phd in mathematics
dastranj.e@gmail.com
Reza
Hejazi
Phd in mathematics
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 arepresented for the solution of forced Duffing equation. The operational matrix of integration forLegendre multiwavelets is presented and is utilized to reduce the solution of Duffing equationto the solution of linear algebraic equations. Illustrative examples are included to demonstratethe 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
Azarbaijan Shahid Madani University
mohamadrezaazizi52@gmail.com
Ali
Khani
Azarbaijan Shahid Madani University
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 subsequentdevelopment 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