Browsing by Author "Alipour, Mohsen"

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Citation Count: Alipour, Mohsen; Baleanu, Dumitru, "Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by Bps Operational Matrices" :
Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations By Bps Operational Matrices
(Hindawi Publishing Corporation, 2013) Alipour, Mohsen; Baleanu, Dumitru; 56389
We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI). The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1.
Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis
(Hindawi LTD, 2014) Alipour, Mohsen; Baleanu, Dumitru; Babaei, Fereshteh; 56389
We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.
Citation Count: Baleanu, Dumitru...et al. (2017). "Motion Of A Spherical Particle In A Rotating Parabola Using Fractional Lagrangian", University Politehnica Of Bucharest Scientific Bulletin-Series A-Applied Mathematics And Physics, Vol. 79, No: 2, pp. 183-192.
Motion Of A Spherical Particle In A Rotating Parabola Using Fractional Lagrangian
(Univ Politehnica Bucharest, 2017) Baleanu, Dumitru; Asad, Jihad H.; Alipour, Mohsen; Blaszczyk, Tomasz; 56389
In this work, the fractional Lagrangian of a particle moving in a rotating parabola is used to obtain the fractional Euler- Lagrange equations of motion where derivatives within it are given in Caputo fractional derivative. The obtained fractional Euler- Lagrange equations are solved numerically by applying the Bernstein operational matrices with Tau method. The results obtained are very good and when the order of derivative closes to 1, they are in good agreement with those obtained in Ref. [10] using Multi step- Differential Transformation Method (Ms-DTM).
Citation Count: Alipour, Mohsen; Arshad, Sadia; Baleanu, Dumitru, "Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4(+)T-Cells", University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, Vol: 78, No. 4, pp. 243-258, (2016).
Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4(+)T-Cells
(Univ Politehnica Bucharest, 2016) Alipour, Mohsen; Arshad, Sadia; Baleanu, Dumitru; 56389
In this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.
Citation Count: Alipour, Mohsen; Arshad, Sadia; Baleanu, Dumitru (2016). "Numerical and bifurcations analysis for multi-order fractional model of HIV infection of CD4+T-cells", UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, Vol. 78, No. 4, pp. 243 - 258.
Numerical and bifurcations analysis for multi-order fractional model of HIV infection of CD4+T-cells
(2016) Alipour, Mohsen; Arshad, Sadia; Baleanu, Dumitru; 56389
In this paper, we solve the dynamical system of HIV infection of CD4+ T-cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate. © 2016, Politechnica University of Bucharest. All rights reserved.
Citation Count: Taleshian, Amir Hose;...et.al. (2022). "Numerical Investigation of Ordinary and Partial Differential Equations with Variable Fractional Order by Bernstein Operational Matrix", International Journal of Applied and Computational Mathematics, Vol.8, No.6.
Numerical Investigation of Ordinary and Partial Differential Equations with Variable Fractional Order by Bernstein Operational Matrix
(2022) Taleshian, Amir Hosein; Alipour, Mohsen; Babakhani, Azizolla; Baleanu, Dumitru; 56389
This research proposes a method to find numerical solutions of the variable-order fractional differential equation. We derived new operational matrix by applying Bernstein polynomials. Then, using this matrix, the method of solving the system of variable-order fractional differential equation and variable-order fractional partial differential equation are presented. Various numerical examples of these problems are provided along with the figures and tables. Finally, the accuracy of the proposed method is evaluated.
Citation Count: Baleanu, D...et al. 2016). Numerical study for fractional euler-lagrange equations of a harmonic oscillator on a moving platform. Acta Physica Polonica A, 130(3), 688-691. http://dx.doi.org/ 10.12693/APhysPolA.130.688
Numerical study for fractional euler-lagrange equations of a harmonic oscillator on a moving platform
(Polish Acad Sciences Inst Physics, 2016) Baleanu, Dumitru; Blaszczyk, Tomasz; Asad, Jihad H.; Alipour, Mohsen
We investigate the fractional harmonic oscillator on a moving platform. We obtained the fractional Euler-Lagrange equation from the derived fractional Lagrangian of the system which contains left Caputo fractional derivative. We transform the obtained differential equation of motion into a corresponding integral one and then we solve it numerically. Finally, we present many numerical simulations.
Citation Count: Baleanu, D...et al. (2015). On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions. Advance in Difference Equations. http://dx.doi.org/10.1186/s13662-015-0651-z
On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions
(Springer International Publishing, 2015) Baleanu, Dumitru; Khan, Hasib; Jafari, Hossein; Khan, Rahmat Ali; Alipour, Mohsen
We investigate sufficient conditions for existence and uniqueness of solutions for a coupled system of fractional order hybrid differential equations (HDEs) with multi-point hybrid boundary conditions given by D-omega(x(t)/H(t, x(t), z(t))) = -K-1 (t, x(t), z(t)), omega epsilon (2, 3], D-epsilon(z(t)/G(t, x(t), z(t))) = -K-2 (t, x(t), z(t)), epsilon epsilon(2, 3] x(t)/H(t, x(t), z(t))vertical bar(t=1) = 0, D-mu(x(t)/H(t, x(t), z(t)))vertical bar(t=delta 1) =0, x((2))(0) = 0 z(t)/G(t, x(t), z(t))vertical bar(t=1) = 0, D-nu(z(t)/G(t, x(t), z(t)))vertical bar(t=delta 2) =0, z((2))(0) = 0 where t epsilon [0, 1], delta(1), delta(2), mu, upsilon epsilon (0, 1), and D-omega, D-epsilon, D-mu and D-upsilon are Caputo's fractional derivatives of order omega, is an element of, mu and nu, respectively, K-1, K-2 epsilon C([0, 1] x R x R, R) and G, H epsilon C([0, 1] x R x R, R - {0}). We use classical results due to Dhage and Banach's contraction principle (BCP) for the existence and uniqueness of solutions. For applications of our results, we include examples.
Citation Count: Alipour, M., Baleanu, D. (2016). On the Kolmogorov forward equations within Caputo and Riemann-Liouville fractions derivatives. Anelele Stiintifice ale Universitatii Ovidius Constanta Matematica, 24(3), 5-19. http://dx.doi.org/10.1515/auom-2016-0045
On the Kolmogorov forward equations within Caputo and Riemann-Liouville fractions derivatives
(Ovidius Univ., 2016) Alipour, Mohsen; Baleanu, Dumitru
In this work, we focus on the fractional versions of the well-known Kolmogorov forward equations. We consider the problem in two cases. In case 1, we apply the left Caputo fractional derivatives for alpha is an element of (0, 1] and in case 2, we use the right Riemann-Liouville fractional derivatives on R+, for alpha is an element of (1, + infinity). The exact solutions are obtained for the both cases by Laplace transforms and stable subordinators.
Citation Count: Baleanu, Dumitru; Asad, Jihad H.; Alipour, Mohsen (2018), On the motion of a heavy bead sliding on a rotating wire - Fractional treatment, Results in Physics, 11, 579-583.
On the motion of a heavy bead sliding on a rotating wire - Fractional treatment
(Elsevier Science BV, 2018) Baleanu, Dumitru; Asad, Jihad H.; Alipour, Mohsen; 56389
In this work, we consider the motion of a heavy particle sliding on a rotating wire. The first step carried for this model is writing the classical and fractional Lagrangian. Secondly, the fractional Hamilton's equations (FHEs) of motion of the system is derived. The fractional equations are formulated in the sense of Caputo. Thirdly, numerical simulations of the FHEs within the fractional operators are presented and discussed for some fractional derivative orders. Numerical results are based on a discretization scheme using the Euler convolution quadrature rule for the discretization of the convolution integral. Finally, simulation results verify that, taking into account the fractional calculus provides more flexible models demonstrating new aspects of the real world phenomena.
Citation Count: Alipour, Mohsen; Rostamy, Davood; Baleanu, Dumitru, "Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices" Journal Of Vibration And Control, Vol.19, No.16, pp.2523-2540, (2013).
Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices
(Sage Publications LTD, 2013) Alipour, Mohsen; Rostamy, Davood; Baleanu, Dumitru; 56389
In this paper, we present a method for solving multi-dimensional fractional optimal control problems. Firstly, we derive the Bernstein polynomials operational matrix for the fractional derivative in the Caputo sense, which has not been done before. The main characteristic behind the approach using this technique is that it reduces the problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The results obtained are in good agreement with the existing ones in the open literature and it is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach 1.
Citation Count: Rostamy, Davood...et al. (2013). "Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis", Romanian Reports in Physics, Vol. 65, No. 2, pp. 334-349.
Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis
(2013) Rostamy, Davood; Alipour, Mohsen; Jafari, Hossein; Baleanu, Dumitru; 56389
In this paper, we present a numerical method for solving a class of fractional differential equations (FDEs). Based on Bernstein Polynomials (BPs) basis, new matrices are utilized to reduce the multi-term orders fractional differential equation to a system of algebraic equations. Convergence analysis is shown by several theorems. Illustrative examples are included to demonstrate the validity and applicability of this method.
Citation Count: Alipour, Mohsen; Baleanu, Dumitru; Karimi, Kobra (2016). "SPECTRAL METHOD BASED ON BERNSTEIN POLYNOMIALS FOR COUPLED SYSTEM OF FREDHOLM INTEGRAL EQUATIONS", APPLIED AND COMPUTATIONAL MATHEMATICS, Vol. 15, No. 2, pp. 212-219.
SPECTRAL METHOD BASED ON BERNSTEIN POLYNOMIALS FOR COUPLED SYSTEM OF FREDHOLM INTEGRAL EQUATIONS
(2016) Alipour, Mohsen; Baleanu, Dumitru; Karimi, Kobra; 56389
In this paper, we apply Bernstein basis to solve the coupled system of Fredholm integral equations (CSFIE). This method transforms the problem to a system of linear algebraic equations that easily solvable. On the other hand, convergence analysis of this method is discussed. the examples show that the proposed method is implemented very simple and the results have high accuracy.
Citation Count: Baleanu, Dumitru; Alipour, Mohsen; Jafari, Hossein, "The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann-Liouville Derivative", Abstract and Applied Analysis, (2013)
The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations With The Riemann-Liouville Derivative
(Hindawi LTD, 2013) Baleanu, Dumitru; Alipour, Mohsen; Jafari, Hossein; 56389
We obtain the approximate analytical solution for the fractional quadratic Riccati differential equation with the Riemann-Liouville derivative by using the Bernstein polynomials (BPs) operational matrices. In this method, we use the operational matrix for fractional integration in the Riemann-Liouville sense. Then by using this matrix and operational matrix of product, we reduce the problem to a system of algebraic equations that can be solved easily. The efficiency and accuracy of the proposed method are illustrated by several examples.
Citation Count: Alipour, Mohsen...et al. (2014). "Variational iteration method for generalized pantograph equation with convergence analysis", Discontinuity, Nonlinearity, and Complexity, Vol. 3, No. 2, pp. 109-121.
Variational iteration method for generalized pantograph equation with convergence analysis
(2014) Alipour, Mohsen; Baleanu, Dumitru; Karimi, Kobra; Kumar, Sunil; 56389
In this paper, we solve generalized pantograph equation by changing the problem to a system of ordinary equations and using the variational iteration method. We discuss convergence of the proposed method to the exact solution. Finally, illustrative examples are given to demonstrate the efficiency of the method.