Browsing by Author "Alipour, M."

Now showing 1 - 5 of 5

Citation - WoS: 1
Citation - Scopus: 2
Motion Of A Spherical Particle In A Rotating Parabola Using Fractional Lagrangian
(Univ Politehnica Bucharest, Sci Bull, 2017) Baleanu, D.; Baleanu, Dumitru; Asad, J. H.; Alipour, M.; Blaszczyk, T.; 56389; Matematik
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 - Scopus: 1
Numerical Investigation of Ordinary and Partial Differential Equations with Variable Fractional Order by Bernstein Operational Matrix
(Springer, 2022) Taleshian, A.H.; Baleanu, Dumitru; Alipour, M.; Babakhani, A.; Baleanu, D.; 56389; Matematik
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. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - WoS: 9
Citation - Scopus: 10
Numerical study for fractional euler-lagrange equations of a harmonic oscillator on a moving platform
(Polish Acad Sciences inst Physics, 2016) Baleanu, D.; Baleanu, Dumitru; Blaszczyk, T.; Asad, J. H.; Alipour, M.; Matematik
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 - Scopus: 60
Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis
(2013) Rostamy, D.; Baleanu, Dumitru; Alipour, M.; Jafari, H.; Baleanu, D.; 56389; Matematik
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 - Scopus: 0
Variational iteration method for generalized pantograph equation with convergence analysis
(L and H Scientific Publishing, LLC, 2014) Alipour, M.; Baleanu, Dumitru; Baleanu, D.; Karimi, K.; Kumar, S.; 56389; Matematik
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. © 2014 L and H Scientific Publishing, LLC.