2017
5
1
1
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Numerical analysis of fractional order model of HIV1 infection of CD4+ Tcells
2
2
In this article, we present a fractional order HIV1 infection model of CD4+ Tcell. 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 HIV1 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 RungeKutta method in case of integer order derivative.
1

1
11


Fazal
Haq
Department of Mathematics,
Hazara University Mansehra, Pakistan
Department of Mathematics,
Hazara University
Pakistan
fazalhaqphd@gmail.com


Kamal
Shah
Department of Mathematics,
University of Malakand, Chakadara Dir(L),
Khyber Pakhtunkhwa, Pakistan
Department of Mathematics,
University of
Pakistan
kamalshah408@gmail.com


GhausUR
Rahman
Department of Mathematics and Statistics,
University of Swat, Pakistan
Department of Mathematics and Statistics,
Universi
Pakistan
r.ghaus@uswat.edu.pk


Muhammad
Shahzad
Department of Mathematics,
Hazara University Mansehra, Pakistan
Department of Mathematics,
Hazara University
Pakistan
shahzadmaths@hu.edu.pk
Infectious diseases models, Fractional Derivatives, Laplace transform , Adomian decomposi tion method
Analytical solution
Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets
2
2
This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving CaputoFabrizio 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 Hdifference that we will be faced it under weak conditions. The method is illustrated by an examples.
1

12
29


Robab
Alikhani
Department of Mathematics,
University of Tabriz, Tabriz, Iran
Department of Mathematics,
University of
I. R. Iran
alikhani@tabrizu.ac.ir
Interval fractional integrodifferential equations
CaputoFabrizio fractional derivative
Method of upper or lower solutions
Fixed point in partially ordered sets
New Solutions for FokkerPlank Equation of Special Stochastic Process via Lie Point Symmetries
2
2
In this paper Lie symmetry analysis is applied in order to find new solutions for Fokker Plank equation of OrnsteinUhlenbeck 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.
1

30
42


Elham
Dastranj
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
Department of Mathematics, Shahrood University
I. R. Iran
dastranj.e@gmail.com


S. Reza
Hejazi
Department of Mathematics, Shahrood University of Technology,
Shahrood, Semnan, Iran
Department of Mathematics, Shahrood University
I. R. Iran
ra.hejazi@gmail.com
Financial market
OrnsteinUhlenbeck
Lie algebra symmetries
FokkerPlank
Numerical solution of the forced Duffing equations using Legendre multiwavelets
2
2
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.
1

43
55


Ramin
Najafi
Department of Mathematics
Maku Branch, Islamic Azad University,
Maku, Iran
Department of Mathematics
Maku Branch, Islamic
I. R. Iran
raminnajafi984@gmail.com


Behzad
Nemati Saray
Faculty of Mathematics,
Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
Faculty of Mathematics,
Institute for Advanced
I. R. Iran
bn.saray@iasbs.ac.ir
Forced Duffing equations
Multiwavelet
Operational matrix of integration
Collocation method
Sinc operational matrix method for solving the BagleyTorvik equation
2
2
The aim of this paper is to present a new numerical method for solving the BagleyTorvik 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 BagleyTorvik 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.
1

56
66


MohammadReza
Azizi
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mathematics, Faculty of Sciences,
Az
I. R. Iran
mohamadrezaazizi52@gmail.com


Ali
Khani
Department of Mathematics, Faculty of Sciences,
Azarbaijan Shahid Madani University, Tabriz, Iran
Department of Mathematics, Faculty of Sciences,
Az
I. R. Iran
khani@azaruniv.edu
BagleyTorvik equation
Sinc functions
Operational matrix
Caputo derivative
Numerical methods
The operational matrix of fractional derivative of the fractionalorder Chebyshev functions and its applications
2
2
In this paper, we introduce a family of fractionalorder 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 fractionalorder 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.
1

67
87


Mohammadreza
Ahmadi Darani
Department of Applied Mathematics, Faculty of Mathematical Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran
Department of Applied Mathematics, Faculty
I. R. Iran
ahmadi.darani@sci.sku.ac.ir


Abbas
Saadatmandi
Department of Applied Mathematics, Faculty of Mathematical Sciences,
University of Kashan, Kashan, 8731751167, Iran
Department of Applied Mathematics, Faculty
I. R. Iran
saadatmandi@kashanu.ac.ir
Chebyshev polynomials
orthogonal system
fractional differential equation
fractionalorder Chebyshev functions
Operational matrix