已认证
2020年发表
- Two-dimensional Müntz–Legendre hybrid functions: theory and applications for solving fractional-order partial differential equations
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Müntz–Legendre hybrid functionsfractional-order partial differential equationsoperational matrix - 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Sohrab-Ali Yousefi
- 发表期刊: computational and applied mathematics
- 论文简介:
- In this manuscript, we present a new numerical technique based on two-dimensional Müntz–Legendre hybrid functions to solve fractional-order partial differential equations (FPDEs) in the sense of Caputo derivative, arising in applied sciences. First, one-dimensional (1D) and two-dimensional (2D) Müntz–Legendre hybrid functions are constructed and their properties are provided, respectively. Next, the Riemann–Liouville operational matrix of 2D Müntz–Legendre hybrid functions is presented. Then, applying this operational matrix and collocation method, the considered equation transforms into a system of algebraic equations. Examples display the efficiency and superiority of the technique for solving these problems with a smooth or non-smooth solution over previous works.
ORCID
2020年发表
- Fibonacci wavelets and Galerkin method to investigate fractional optimal control problems with bibliometric analysis
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fractional optimal control problemsGalerkin methodinequality constraintswavelets - 作者: Sedigheh Sabermahani, Yadollah Ordokhani
- 发表期刊: Journal of Vibration and Control
- 论文简介:
- This study presents a computational method for the solution of the fractional optimal control problems subject to fractional systems with equality and inequality constraints. The proposed procedure is based upon Fibonacci wavelets. The fractional derivative is described in the Caputo sense. The Riemann–Liouville operational matrix for Fibonacci wavelets is obtained. Then, we use this operational matrix and the Galerkin method to reduce the given problem into a system of algebraic equations. We discuss the convergence of the algorithm. Several numerical examples are included to observe the validity, effectiveness, and accuracy of the suggested scheme. Moreover, fractional optimal control problems are studied through a bibliometric viewpoint.
ORCID
2020年发表
- A new operational matrix of Muntz-Legendre polynomials and Petrov-Galerkin method for solving fractional Volterra-Fredholm integro-differential equations
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Müntz-Legendre polynomialsVolterra-Fredholm integro-differential equationsPetrov-Galerkin methodnumerical method - 作者: Sedigheh Sabermahani, Yadollah Ordokhani
- 发表期刊: Computational Methods for Differential Equations
- 论文简介:
- This manuscript is devoted to present an efficient numerical method for finding numerical solution of Volterra-Fredholm integro-differential equations of fractional order. This technique is based on applying Müntz-Legendre polynomials and Petrov-Galerkin method. A new Riemann-Liouville operational matrix for Müntz-Legendre polynomials is proposed using Laplace transform. Employing this operational matrix and Petrov-Galerkin method, transforms the problem into a system of algebraic equations. Next, we solve this system by applying any iterative method. An estimation of the error is proposed. Moreover, some numerical examples are implemented in order to show the validity and accuracy of the suggested method.
ORCID
2019年发表
- Fibonacci wavelets and their applications for solving two classes of time-varying delay problems
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waveletsPetrov‐Galerkin methodNewton's iterative methodoptimal control problems - 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Sohrab‐Ali Yousefi
- 发表期刊: Optimal Control Applications and Methods
- 论文简介:
- In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique.
ORCID
2019年发表
- Fractional-order Lagrange polynomials: An application for solving delay fractional optimal control problems
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Lagrange polynomialsfractional optimal control problemsdelayoperational matrix - 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Sohrab-Ali Yousefi
- 发表期刊: Transactions of the Institute of Measurement and Control
- 论文简介:
- The main purpose of this work is to provide an efficient method for solving delay fractional optimal control problems (DFOCPs). Our method is based on fractional-order Lagrange polynomials (FLPs) and the collocation method. The FLPs are used to achieve a new operational matrix of fractional derivative. Also, we present a delay operational matrix of FLPs. These operational matrices are driven without considering the nodes of Lagrange polynomials. The operational matrices and collocation method are applied to a constrained extremum in order to minimize the performance index. Then, the problem reduces to the solution of a system of algebraic equations. Convergence of the algorithm and approximation of FLPs are proposed. Furthermore, the upper bound of the error for the operational matrix of fractional derivatives is obtained. Numerical tests for demonstrating the efficiency and effectiveness of the method …
ORCID
2019年发表
- Fractional-order general Lagrange scaling functions and their applications
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general Lagrange scaling functionsNewton’s iterative methodoperational matrixcollocation method - 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Sohrab Ali Yousefi
- 发表期刊: BIT Numerical Mathematics
- 论文简介:
- In this study, a general formulation for the fractional-order general Lagrange scaling functions (FGLSFs) is introduced. These functions are employed for solving a class of fractional differential equations and a particular class of fractional delay differential equations. For this approach, we derive FGLSFs fractional integration and delay operational matrices. These operational matrices and collocation method are utilized to reduce each of the problems to a system of algebraic equation, which can be solve employing Newton’s iterative method. We indicate convergence of this method. Finally, some illustrative examples in order to observe the validity, effectiveness and accuracy of the present technique are included. Also, by applying this method, we solve the mathematical model of the noise effect on the laser device.
ORCID
2019年发表
- Fractional-order Fibonacci-hybrid functions approach for solving fractional delay differential equations
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hybrid functionsFibonacci polynomialsoperational matrixdelay - 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Sohrab-Ali Yousefi
- 发表期刊: Engineering with Computers
- 论文简介:
- The aim of the current paper is to propose an efficient method for finding the approximate solution of fractional delay differential equations. This technique is based on hybrid functions of block-pulse and fractional-order Fibonacci polynomials. First, we define fractional-order Fibonacci polynomials. Next, using Fibonacci polynomials of fractional-order, we introduce a new set of basis functions. These new functions are called fractional-order Fibonacci-hybrid functions (FFHFs) which are appropriate for the approximation of smooth and piecewise smooth functions. The Riemann–Liouville integral operational matrix and delay operational matrix of the FFHFs are obtained. Then, using these matrices and collocation method, the problem is reduced to a system of algebraic equations. Using Newton’s iterative method, we solve this system. Some examples are proposed to test the efficiency and effectiveness of the present …
已认证
2019年发表
- A Novel Lagrange Operational Matrix and Tau-Collocation Method for Solving Variable-Order Fractional Differential Equations
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Tau-Collocation methodLagrange polynomialsvariable-orderdifferential equations - 作者: S. Sabermahani, Y. Ordokhani, P. M. Lima
- 发表期刊: Iranian Journal of Science and Technology Transaction A-Science
- 论文简介:
- The main result achieved in this paper is an operational Tau-Collocation method based on a class of Lagrange polynomials. The proposed method is applied to approximate the solution of variable-order fractional differential equations (VOFDEs). We achieve operational matrix of the Caputo’s variable-order derivative for the Lagrange polynomials. This matrix and Tau-Collocation method are utilized to transform the initial equation into a system of algebraic equations. Also, we discuss the numerical solvability of the Lagrange-Tau algebraic system in the case of a variable-order linear equation. Error estimates are presented. Some examples are provided to illustrate the accuracy and computational efficiency of the present method to solve VOFDEs. Moreover, one of the numerical examples is concerned with the shape-memory polymer model.
ORCID
2018年发表
- Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations
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Lagrange polynomialsFractional differential equationsoperational matrixcollocation method - 作者: Sedigheh Sabermahani, Y Ordokhani, SA Yousefi
- 发表期刊: Computational and Applied Mathematics
- 论文简介:
- In this study, we propose a new set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Fractional differential equations are the best tools for modelling natural phenomenon that are elaborated by fractional calculus. Therefore, we need an accurate and efficient technique for solving them. The main purpose of this article is to generalize new functions based on Lagrange polynomials to the fractional calculus. At first, we present a new representation of Lagrange polynomials and in continue, we propose a new set of fractional-order functions which are called fractional-order Lagrange polynomials (FLPs). Besides, a general formulation for operational matrices of fractional integration and derivative of FLPs on arbitrary nodal points are extracted. These matrices are obtained using Laplace transform. The initial value problems is reduced to the system of …