Browsing by Author "Sayevand, Khosro"

Now showing 1 - 6 of 6

A novel difference schemes for analyzing the fractional Navier- Stokese quations
(Ovidius Univ Press, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Sahsavand, Fatemeh; 56389
In this report, a novel difference scheme is used to analyzing the Navier - Stokes problems of fractional order. Existence and uniqueness of the suggested approach with a Lipschitz condition and Picard theorem are proved. Furthermore, we find a discrete analogue of the derivative and then stability and convergence of our strategy in multi dimensional domain are proved.
A numerical approach for solving fractional optimal control problems with mittag-leffler kernel
(2021) Baleanu, Dumitru; Ganji, Roghayeh M.; Sayevand, Khosro; Baleanu, Dumitru; 56389
In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana-Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.
A Perturbative Analysis Of Nonlinear Cubic-Quintic Duffing Oscillators
(Editura Academiei Romane, 2014) Baleanu, Dumitru; Baleanu, Dumitru; Fardi, Mojtaba; 56389
Duffing oscillators comprise one of the canonical examples of Hamilton systems. The presence of a quintic term makes the cubic-quintic Duffing oscillator more complex and interesting to study. In this paper, the homotopy analysis method (HAM) is used to obtain the analytical solution for the nonlinear cubic-quintic Duffing oscillators. The HAM helps to obtain the frequency omega in the form of approximation series of a convergence control parameter (h) over bar. The valid region of (h) over bar is determined by plotting the omega - (h) over bar curve and afterwards we compared the obtained results with the exact solutions.
Homotopy Analysis Method For Solving Abel Differential Equation of Fractional Order
(Sciendo, 2013) Baleanu, Dumitru; Sayevand, Khosro; Tajadodi, Haleh; Baleanu, Dumitru; 56389
In this study, the homotopy analysis method is used for solving the Abel differential equation with fractional order within the Caputo sense. Stabilityand convergence of the proposed approach is investigated. The numerical results demonstrate that the homotopy analysis method is accurate and readily implemented.
Performance evaluation of matched asymptotic expansions for fractional differential equations with multi-order
(Soc Matematice Romania, 2016) Baleanu, Dumitru; Sayevand, Khosro
An extension of the concept of the asymptotic expansions method is presented in this paper. The multi-order differential equations of fractional order are investigated and the convergence of the proposed method is proven. The reported results show that the present approach is very effective and accurate and also are in good agreement with the ones in the literature.
Travelling Wave Solutions: A New Approach To The Analysis of Nonlinear Physical Phenomena
(Sciendo, 2014) Baleanu, Dumitru; Baleanu, Dumitru; Fardi, Mojtaba; 56389
In this manuscript, a reliable scheme based on a general functional transformation is applied to construct the exact travelling wave solution for nonlinear differential equations. Our methodology is investigated by means of the modified homotopy analysis method which contains two convergence-control parameters. The obtained results reveal that the proposed approach is a very effective. Several illustrative examples are investigated in detail.