ORIGINAL_ARTICLE
Numerical analysis of fractional order model of HIV-1 infection of CD4+ T-cells
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.
http://cmde.tabrizu.ac.ir/article_5825_f4866fc1855d93e48a17375f970401ef.pdf
2017-01-01T11:23:20
2018-11-13T11:23:20
1
11
Infectious diseases models, Fractional Derivatives, Laplace transform , Adomian decomposi- tion method
Analytical solution
Fazal
Haq
fazalhaqphd@gmail.com
true
1
Department of Mathematics,
Hazara University Mansehra, Pakistan
Department of Mathematics,
Hazara University Mansehra, Pakistan
Department of Mathematics,
Hazara University Mansehra, Pakistan
LEAD_AUTHOR
Kamal
Shah
kamalshah408@gmail.com
true
2
Department of Mathematics,
University of Malakand, Chakadara Dir(L),
Khyber Pakhtunkhwa, Pakistan
Department of Mathematics,
University of Malakand, Chakadara Dir(L),
Khyber Pakhtunkhwa, Pakistan
Department of Mathematics,
University of Malakand, Chakadara Dir(L),
Khyber Pakhtunkhwa, Pakistan
AUTHOR
Ghaus-UR-
Rahman
r.ghaus@uswat.edu.pk
true
3
Department of Mathematics and Statistics,
University of Swat, Pakistan
Department of Mathematics and Statistics,
University of Swat, Pakistan
Department of Mathematics and Statistics,
University of Swat, Pakistan
AUTHOR
Muhammad
Shahzad
shahzadmaths@hu.edu.pk
true
4
Department of Mathematics,
Hazara University Mansehra, Pakistan
Department of Mathematics,
Hazara University Mansehra, Pakistan
Department of Mathematics,
Hazara University Mansehra, Pakistan
AUTHOR
ORIGINAL_ARTICLE
Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets
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.
http://cmde.tabrizu.ac.ir/article_5832_a153da52e918984455148c1c2bcc3054.pdf
2017-01-01T11:23:20
2018-11-13T11:23:20
12
29
Interval fractional integrodifferential equations
Caputo-Fabrizio fractional derivative
Method of upper or lower solutions
Fixed point in partially ordered sets
Robab
Alikhani
alikhani@tabrizu.ac.ir
true
1
Department of Mathematics,
University of Tabriz, Tabriz, Iran
Department of Mathematics,
University of Tabriz, Tabriz, Iran
Department of Mathematics,
University of Tabriz, Tabriz, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
New Solutions for Fokker-Plank Equation of Special Stochastic Process via Lie Point Symmetries
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.
http://cmde.tabrizu.ac.ir/article_5860_0619691dc5e6d56d4bebd5478457bf27.pdf
2017-01-01T11:23:20
2018-11-13T11:23:20
30
42
Financial market
Ornstein-Uhlenbeck
Lie algebra symmetries
Fokker-Plank
Elham
Dastranj
dastranj.e@gmail.com
true
1
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
LEAD_AUTHOR
S. Reza
Hejazi
ra.hejazi@gmail.com
true
2
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
AUTHOR
ORIGINAL_ARTICLE
Numerical solution of the forced Duffing equations using Legendre multiwavelets
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.
http://cmde.tabrizu.ac.ir/article_5861_ca3f0ed7de5017b87aa945ff661cf787.pdf
2017-01-01T11:23:20
2018-11-13T11:23:20
43
55
Forced Duffing equations
Multiwavelet
Operational matrix of integration
Collocation method
Ramin
Najafi
raminnajafi984@gmail.com
true
1
Department of Mathematics
Maku Branch, Islamic Azad University,
Maku, Iran
Department of Mathematics
Maku Branch, Islamic Azad University,
Maku, Iran
Department of Mathematics
Maku Branch, Islamic Azad University,
Maku, Iran
LEAD_AUTHOR
Behzad
Nemati Saray
bn.saray@iasbs.ac.ir
true
2
Faculty of Mathematics,
Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
Faculty of Mathematics,
Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
Faculty of Mathematics,
Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
AUTHOR
ORIGINAL_ARTICLE
Sinc operational matrix method for solving the Bagley-Torvik equation
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.
http://cmde.tabrizu.ac.ir/article_5868_fdcacac6135f0bb82c1b80f8d91e4a6b.pdf
2017-01-01T11:23:20
2018-11-13T11:23:20
56
66
Bagley-Torvik equation
Sinc functions
Operational matrix
Caputo derivative
Numerical methods
Mohammad-Reza
Azizi
mohamadrezaazizi52@gmail.com
true
1
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
LEAD_AUTHOR
Ali
Khani
khani@azaruniv.edu
true
2
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
AUTHOR
ORIGINAL_ARTICLE
The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications
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.
http://cmde.tabrizu.ac.ir/article_5902_97563e2dfae2abcda93be4bd14ba9e1c.pdf
2017-01-01T11:23:20
2018-11-13T11:23:20
67
87
Chebyshev polynomials
orthogonal system
fractional differential equation
fractional-order Chebyshev functions
Operational matrix
Mohammadreza
Ahmadi Darani
ahmadi.darani@sci.sku.ac.ir
true
1
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
LEAD_AUTHOR
Abbas
Saadatmandi
saadatmandi@kashanu.ac.ir
true
2
Department of Applied Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan, 87317-51167, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan, 87317-51167, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan, 87317-51167, Iran
AUTHOR