WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
Browse
8 results
Search Results
Article Citation - WoS: 66Citation - Scopus: 63An Accurate Numerical Technique for Solving Fractional Optimal Control Problems(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; MatematikIn this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.Article Citation - WoS: 26A Chebyshev-Laguerre Collocation Scheme for Solving A Time Fractional Sub-Diffusion Equation on A Semi-Infinite Domain(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Abdelkawy, M. A.; Alzahrani, A. A.; Baleanu, D.; Alzahrani, E. O.; MatematikWe propose a new efficient spectral collocation method for solving a time fractional sub-diffusion equation on a semi-infinite domain. The shifted Chebyshev-Gauss-Radau interpolation method is adapted for time discretization along with the Laguerre-Gauss-Radau collocation scheme that is used for space discretization on a semi-infinite domain. The main advantage of the proposed approach is that a spectral method is implemented for both time and space discretizations, which allows us to present a new efficient algorithm for solving time fractional sub-diffusion equations.Article Citation - WoS: 37Citation - Scopus: 40The Analytical Investigation of Time-Fractional Multi-Dimensional Navier-Stokes Equation(Elsevier, 2020) Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, RasoolIn the present research article, we implemented two well-known analytical techniques to solve fractional-order multi-dimensional Navier-Stokes equation. The proposed methods are the modification of Adomian decomposition method and variational iteration method by using natural transformation. Furthermore, some illustrative examples are presented to confirm the validity of the suggested methods. The solutions graphs and tables are constructed for both fractional and integer-order problems. It is investigated that the suggested techniques have the identical solutions of the problems. The solution comparison via graphs and tables have also supported the greater accuracy and higher rate of convergence of the present methods. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.Article Citation - WoS: 5Citation - Scopus: 4Existence Results for Coupled Differential Equations of Non-Integer Order With Riemann-Liouville, Erdelyi-Kober Integral Conditions(Amer inst Mathematical Sciences-aims, 2021) Hemalatha, S.; Duraisamy, P.; Pandiyan, P.; Muthaiah, Subramanian; Baleanu, DumitruThis paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdelyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed.Article Citation - WoS: 31Citation - Scopus: 39Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique(Frontiers Media Sa, 2020) Farooq, Umar; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, RasoolIn the present article, fractional view of third order Kortewege-De Vries equations is presented by a sophisticated analytical technique called Mohand decomposition method. The Caputo fractional derivative operator is used to express fractional derivatives, containing in the targeted problems. Some numerical examples are presented to show the effectiveness of the method for both fractional and integer order problems. From the table, it is investigated that the proposed method has the same rate of convergence as compare to homotopy perturbation transform method. The solution graphs have confirmed the best agreement with the exact solutions of the problems and also revealed that if the sequence of fractional-orders is approaches to integer order, then the fractional order solutions of the problems are converge to an integer order solution. Moreover, the proposed method is straight forward and easy to implement and therefore can be used for other non-linear fractional-order partial differential equations.Article Citation - WoS: 34Citation - Scopus: 41Analytical Solutions of (2+time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method(Mdpi, 2020) Farooq, Umar; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Khan, HassanIn this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by using the suggested method which provides the desired rate of convergence. Some numerical examples are solved by using the proposed method. The solutions of the targeted problems are represented by graphs which have confirmed closed contact between the exact and obtained solutions of the problems. Based on the novelty and straightforward implementation of the method, it is considered to be one of the best analytical techniques to solve linear and non-linear fractional partial differential equations.Article Citation - WoS: 37Citation - Scopus: 38A New Analytical Technique To Solve System of Fractional-Order Partial Differential Equations(Ieee-inst Electrical Electronics Engineers inc, 2019) Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; Shah, RasoolIn this research article, a new analytical technique is implemented to solve system of fractional-order partial differential equations. The fractional derivatives are carried out with the help of Caputo fractional derivative operator. The direct implementation of Mohand and its inverse transformation provide sufficient easy less and reliability of the proposed method. Decomposition method along with Mohand transformation is proceeded to attain the analytical solution of the targeted problems. The applicability of the suggested method is analyzed through illustrative examples. The solutions graph has the best contact with the graphs of exact solutions in paper. Moreover, the convergence of the present technique is sufficiently fast, so that it can be considered the best technique to solve system of nonlinear fractional-order partial differential equations.Article Citation - WoS: 67Citation - Scopus: 82A Numerical Approach Based on Legendre Orthonormal Polynomials for Numerical Solutions of Fractional Optimal Control Problems(Sage Publications Ltd, 2017) Doha, E. H.; Baleanu, D.; Bhrawy, A. H.; Ezz-Eldien, S. S.The numerical solution of a fractional optimal control problem having a quadratic performance index is proposed and analyzed. The performance index of the fractional optimal control problem is considered as a function of both the state and the control variables. The dynamic constraint is expressed as a fractional differential equation that includes an integer derivative in addition to the fractional derivative. The order of the fractional derivative is taken as less than one and described in the Caputo sense. Based on the shifted Legendre orthonormal polynomials, we employ the operational matrix of fractional derivatives, the Legendre-Gauss quadrature formula and the Lagrange multiplier method for reducing such a problem into a problem consisting of solving a system of algebraic equations. The convergence of the proposed method is analyzed. For confirming the validity and accuracy of the proposed numerical method, a numerical example is presented along with a comparison between our numerical results and those obtained using the Legendre spectral-collocation method.