Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 23Citation - Scopus: 23A Computationally Efficient Method for A Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions(Editura Acad Romane, 2018) El-Kalaawy, A. A.; Doha, E. H.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Zaky, M. A.This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.Article Citation - WoS: 3Citation - Scopus: 3On Ritz Approximation for a Class of Fractional Optimal Control Problems(World Scientific Publ Co Pte Ltd, 2022) Jafari, Hossein; Johnston, Sarah Jane; Baleanu, Dumitru; Firoozjaee, Mohammad ArabWe apply the Ritz method to approximate the solution of optimal control problems through the use of polynomials. The constraints of the problem take the form of differential equations of fractional order accompanied by the boundary and initial conditions. The ultimate goal of the algorithm is to set up a system of equations whose number matches the unknowns. Computing the unknowns enables us to approximate the solution of the objective function in the form of polynomials.Article Citation - WoS: 16Citation - Scopus: 20Different Strategies To Confront Maize Streak Disease Based on Fractional Optimal Control Formulation(Pergamon-elsevier Science Ltd, 2022) Baleanu, Dumitru; Ali, Hegagi Mohamed; Ameen, Ismail GadIn this paper, we propose a general formulation for the transmission dynamics of maize streak virus (MSV) pathogen interaction with a pest invasion in the maize plant. The mathematical formalism for this model is dependent on Caputo fractional operator with modification of its parameters. In the considered model, the total population of maize plants is divided into two classes: susceptible, infected maize and the total population of leafhopper vector contains two compartments: susceptible, infected leafhopper vector, with a compartment for MSV pathogen. In addition, this fractional-order model (FOM) is involving the proportion of three controls u1, u2 and u3 which namely respectively prevention, quarantine and chemical control. We present the positivity and boundedness of the projected solutions to assure the feasibility of solutions of this FOM. The control reproduction number (Rc) is derived by next generation matrix (NGM) method and showed graphically the effect of the controls for each proposed strategy on the behavior of Rc. The local stability analysis for all possible equilibrium points (EPs) has been examined in detail. Moreover, the fractional optimal control problem (FOCP) is characterized and fractional necessary optimality conditions (NOCs) are derived by using Pontryagin's maximum principle (PMP). These NOCs are solved numerically, where the state and co -state equations based on the left Caputo fractional derivative (CFD). We offer four strategies to illustrate the effects of the proposed controls to investigate the preferable strategy for the elimination of maize streak disease (MSD), as each one of these strategies is able to alleviate this disease at a specific time. Finally, simulations are performed utilizing MATLAB with realistic ecological parameter values to demonstrate the obtained theoretical results. Comparative studies illustrated that infection of maize plants can be reduced through the proposed model, which has a significant impact on plant epidemiology.Article Citation - WoS: 33Citation - Scopus: 36Shifted Ultraspherical Pseudo-Galerkin Method for Approximating the Solutions of Some Types of Ordinary Fractional Problems(Springer, 2021) Mahmoud, Doha; Baleanu, Dumitru; El-kady, Mamdouh; Abdelhakem, MohamedIn this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods. Also, this method can be extended to approximate fractional integro-differential equations (FIDEs) and fractional optimal control problems (FOCPs). The spatial approximations with their derivatives are based on shifted ultraspherical polynomials (SUPs). Modified Galerkin spectral method has been used to create direct approximate solutions of linear/nonlinear ordinary fractional differential equations, a system of ordinary fraction differential equations, fractional integro-differential equations, or fractional optimal control problems. The aim is to transform those problems into a system of algebraic equations. That system will be efficiently solved by any solver. Three spaces of collocation nodes have been used through that transformation. Finally, numerical examples show the accuracy and efficiency of the investigated method.Article Citation - WoS: 42Citation - Scopus: 44A Numerical Approach for Solving Fractional Optimal Control Problems With Mittag-Leffler Kernel(Sage Publications Ltd, 2022) Ganji, Roghayeh M.; Sayevand, Khosro; Baleanu, Dumitru; Jafari, HosseinIn 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.Article Citation - WoS: 86Citation - Scopus: 93Solving Multi-Dimensional Fractional Optimal Control Problems With Inequality Constraint by Bernstein Polynomials Operational Matrices(Sage Publications Ltd, 2013) Rostamy, Davood; Baleanu, Dumitru; Alipour, MohsenIn 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.Article A Computationally Efficient Method For a Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions(Editura Academiei Romane, 2018) El-Kalaawy, Ahmed A.; Doha, Eid H.; Ezz-Eldien, Samer S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Baleanu, Dumitru; Zaky, M. A.This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.Article Citation - WoS: 111Citation - Scopus: 122A Hybrid Functions Numerical Scheme for Fractional Optimal Control Problems: Application To Nonanalytic Dynamic Systems(Sage Publications Ltd, 2018) Moradi, L.; Baleanu, D.; Jajarmi, A.; Mohammadi, F.In this paper, a numerical scheme based on hybrid Chelyshkov functions (HCFs) is presented to solve a class of fractional optimal control problems (FOCPs). To this end, by using the orthogonal Chelyshkov polynomials, the HCFs are constructed and a general formulation for their operational matrix of the fractional integration, in the Riemann-Liouville sense, is derived. This operational matrix together with HCFs are used to reduce the FOCP to a system of algebraic equations, which can be solved by any standard iterative algorithm. Moreover, the application of presented method to the problems with a nonanalytic dynamic system is investigated. Numerical results confirm that the proposed HCFs method can achieve spectral accuracy to approximate the solution of FOCPs.Article Citation - WoS: 35Citation - Scopus: 40Shifted Chebyshev Schemes for Solving Fractional Optimal Control Problems(Sage Publications Ltd, 2019) Moussa, H.; Baleanu, D.; El-Kady, M.; Abdelhakem, M.Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.