2018-08-17T19:17:08Z
http://cmde.tabrizu.ac.ir/?_action=export&rf=summon&issue=827
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2017
5
1
Numerical analysis of fractional order model of HIV-1 infection of CD4+ T-cells
Fazal
Haq
Kamal
Shah
Ghaus-UR-
Rahman
Muhammad
Shahzad
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
2017
01
01
1
11
http://cmde.tabrizu.ac.ir/article_5825_f4866fc1855d93e48a17375f970401ef.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2017
5
1
Interval fractional integrodifferential equations without singular kernel by fixed point in partially ordered sets
Robab
Alikhani
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
2017
01
01
12
29
http://cmde.tabrizu.ac.ir/article_5832_a153da52e918984455148c1c2bcc3054.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2017
5
1
New Solutions for Fokker-Plank Equation of Special Stochastic Process via Lie Point Symmetries
Elham
Dastranj
S. Reza
Hejazi
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
2017
01
01
30
42
http://cmde.tabrizu.ac.ir/article_5860_0619691dc5e6d56d4bebd5478457bf27.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2017
5
1
Numerical solution of the forced Duffing equations using Legendre multiwavelets
Ramin
Najafi
Behzad
Nemati Saray
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
2017
01
01
43
55
http://cmde.tabrizu.ac.ir/article_5861_ca3f0ed7de5017b87aa945ff661cf787.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2017
5
1
Sinc operational matrix method for solving the Bagley-Torvik equation
Mohammad-Reza
Azizi
Ali
Khani
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
2017
01
01
56
66
http://cmde.tabrizu.ac.ir/article_5868_fdcacac6135f0bb82c1b80f8d91e4a6b.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2017
5
1
The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications
Mohammadreza
Ahmadi Darani
Abbas
Saadatmandi
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
2017
01
01
67
87
http://cmde.tabrizu.ac.ir/article_5902_97563e2dfae2abcda93be4bd14ba9e1c.pdf