2017
5
1
1
0
Numerical analysis of fractional order model of HIV1 infection of CD4+ Tcells
2
2
In this article, we present a fractional order HIV1 infectionmodel of CD4+ Tcell. 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 HIV1 model in the form of infinite series. The concernedseries rapidly converges to its exact value. Moreover, we compare ourresults with the results obtained by RungeKutta method in case of integerorder derivative.
1

1
11


Fazal
Haq
Hazara University
Hazara University
Pakistan
fazalhaqphd@gmail.com


Kamal
Shah
University of Malakand
University of Malakand
Pakistan
kamalshah408@gmail.com


Ghausur
rahman
University of Swat
University of Swat
Pakistan
r.ghaus@uswat.edu.pk


Muhammad
Shahzad
Hazara University
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 initialvalue problem of interval fractional integrodifferential equationsinvolving CaputoFabrizio 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 Hdifference that we will be faced it under weakconditions. The method is illustrated by an examples.
1

12
29


Robab
Alikhani
Department of Applied Mathematics Faculty of Mathematical Sciences University of Tabriz
Department of Applied Mathematics Faculty
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.
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30
42


Elham
Dastranj
Phd in mathematics
Phd in mathematics
I. R. Iran
dastranj.e@gmail.com


Reza
Hejazi
Phd in mathematics
Phd in mathematics
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 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.
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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 subsequentdevelopment 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.
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56
66


MohammadReza
Azizi
Azarbaijan Shahid Madani University
Azarbaijan Shahid Madani University
I. R. Iran
mohamadrezaazizi52@gmail.com


Ali
Khani
Azarbaijan Shahid Madani University
Azarbaijan Shahid Madani University
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.
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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