ORCID
2023年发表
- Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems
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fractional optimal control problems
Atangana–Riemann–Liouville derivative
Ritz method
pseudo-operational matrix
- 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Parisa Rahimkhani
- 发表期刊: Chaos, Solitons & Fractals
- 论文简介:
- Different types of fractional derivatives have recently been noticed by researchers and used in modeling phenomena due to their characteristics. Furthermore, fractional optimal control problems have been the focus of many researchers because they reflect the real nature of different models. Hence, this article considers a class of nonlinear fractal-fractional optimal control problems in the Atangana–Riemann–Liouville sense with the Mittag-Leffler non-singular kernel. In this study, a numerical method based on the generalized Lucas wavelets and the Ritz method is presented to obtain approximate solutions. Then, the generalized Lucas wavelets and an extra pseudo-operational matrix of the Atangana–Riemann–Liouville derivative are introduced. We demonstrate the advantage of the proposed method through three numerical examples.
ORCID
2023年发表
- Fractional-Order Mittag–Leffler Functions for Solving Multi-dimensional Fractional Pantograph Delay Differential Equations
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fractional-order Mittag–Leffler functions
pantograph differential equation
pseudo-operational matrix
collocation method
- 作者: Arezoo Ghasempour, Yadollah Ordokhani, Sedigheh Sabermahani
- 发表期刊: Iranian Journal of Science
- 论文简介:
- This manuscript is devoted to presenting an approximation method based upon a new set of fractional functions named fractional-order Mittag–Leffler functions (FM-LFs). This scheme is implemented to approximate the solution of a multi-dimensional fractional pantograph differential equation. To this approach, FM-LFs are introduced. Then, we employ FM-LFs to construct the pseudo-operational matrix of fractional integration and pantograph operational matrix (P-OM). We reduce the considered problems to systems of algebraic equations with the help of the mentioned matrices, and the collocation technique, respectively. Error analysis is proposed. Moreover, several numerical experiments have been considered to confirm the efficiency and applicability of the suggested scheme.
ORCID
2023年发表
- Hahn hybrid functions for solving distributed order fractional Black–Scholes European option pricing problem arising in financial market
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hybrid functions
distributed order
Gauss–Legendre quadrature formula
Black–Scholes option pricing
- 作者: Parisa Rahimkhani, Yadollah Ordokhani, Sedigheh Sabermahani
- 发表期刊: Mathematical Methods in the Applied Sciences
- 论文简介:
- The main purpose of this work is to present a new numerical method based on Hahn hybrid functions (HHFs) for solving of Black–Scholes option pricing distributed order time‐fractional partial differential equation. To this end, HHFs are introduced and their fractional integral operator with some properties of HHFs is calculated. In the next, with the help of fractional integral operator of HHFs, Gauss–Legendre quadrature formula and collocation method, distributed order time‐fractional Black–Scholes model is reduced to a system of algebraic equations. Furthermore, convergence analysis of the mentioned scheme is discussed. Finally, some test problems have been included to confirm the validity and efficiency of the mentioned numerical scheme. Moreover, Black–Scholes equations are studied through a bibliometric viewpoint.
ORCID
2023年发表
- Ritz-generalized Pell wavelet method: Application for two classes of fractional pantograph problems
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wavelets
pantograph differential equations
optimal control problems
Ritz and collocation methods
- 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Mohsen Razzaghi
- 发表期刊: Communications in Nonlinear Science and Numerical Simulation
- 论文简介:
- In this work, a computational method for solving fractional pantograph differential equations and fractional pantograph optimal control problems is proposed. The present technique is based on a new set of wavelet functions and a combination of Ritz and collocation methods. To this aim, we construct generalized Pell wavelets (GPws). An extra Caputo pseudo-operational matrix and pantograph operational matrix of GPws as new achievements are presented. To more easily calculate the fractional derivative of GPws, we define generalized piecewise Taylor functions (GPTfs). Then, utilizing these matrices, the Ritz method, and the collocation method, we find an approximate solution for each of the considered problems. An error analysis is proposed. Finally, some illustrative numerical tests are given to display the accuracy and effectiveness of the developed scheme.
ORCID
2023年发表
- Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method
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distributed-order
optimal control problems
operational matrix
wavelets
- 作者: Sedigheh Sabermahani, Yadollah Ordokhani
- 发表期刊: Journal of Vibration and Control
- 论文简介:
- A new approach to finding the approximate solution of distributed-order fractional optimal control problems (D-O FOCPs) is proposed. This method is based on Fibonacci wavelets (FWs). We present a new Riemann–Liouville operational matrix for FWs using the hypergeometric function. Using this, an operational matrix of the distributed-order fractional derivative is presented. Implementing the mentioned operational matrix with the help of the Gauss–Legendre numerical integration, the problem converts to a system of algebraic equations. Error analysis is proposed. Finally, the validation of the present technique is checked by solving some numerical examples.
已认证
2022年发表
- Touchard wavelet technique for solving time-fractional Black–Scholes model
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time-fractional Black–Scholes equations
wavelets
pseudo-operational matrix
numerical method
- 作者: Farshid Nourian, Mehrdad Lakestani, Sedigheh Sabermahani, Yadollah Ordokhani
- 发表期刊: COMPUTATIONAL & APPLIED MATHEMATICS
- 论文简介:
- The main idea of this study is to introduce a novel set of wavelet functions named Touchard wavelets for solving time-fractional Black–Scholes equations. The numerical method is discussed based on the pseudo-operational matrix of Riemann–Liouville fractional integration and the least square approximation method. The methodology of deriving the pseudo-operational matrix is calculated accurately and this has a direct effect on the accuracy of the method. The error estimation is proposed. At last, two numerical experiments are employed to clarify the performance and high accuracy of the present technique.
已认证
2022年发表
- Application of Two-Dimensional Fibonacci Wavelets in Fractional Partial Differential Equations Arising in the Financial Market
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wavelets
fractional Black–Scholes equations
Riemann–Liouville pseudo-operational matrix
bibliometric analysis
- 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Parisa Rahimkhani
- 发表期刊: International Journal of Applied and Computational Mathematics
- 论文简介:
- This manuscript provides an efficient and high-accuracy computational technique for solving fractional Black–Scholes equations (FB–SEs) arising in the financial market. In order to find an accurate solution of the mentioned equations, we use the collocation method through the two-dimensional Fibonacci wavelets (2D-FWs). To carry out the scheme, we firstly present 2D-FWs. Then, Riemann–Liouville pseudo-operational matrix for 1 & 2D-FW are achieved. RL pseudo-operational matrix for 2D-FWs and the collocation technique are employed to reduce the mentioned problem into a system of algebraic equations. Moreover, the convergence of the approximate solution to the exact solution is proven by providing an upper bound of error estimate. To reveal the performance and accuracy of the developed method, some numerical experiments are provided. Moreover, we present a brief bibliometric analysis and …
ORCID
2022年发表
- Solution of optimal control problems governed by volterra integral and fractional integro-differential equations
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wavelets
optimal control problems
fractional Volterra integro-differential equations
Volterra integral equations
- 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Kobra Rabiei, Mohsen Razzaghi
- 发表期刊: Journal of Vibration and Control
- 论文简介:
- In this manuscript, we investigate two categories of optimal control problems (OCPs), OPCs via fractional Volterra integro-differential equations and Volterra integral equations. Touchard wavelets as an appropriate class of bases are defined to develop a new hybrid scheme for the considered problems. To this approach, Riemann–Liouville fractional integral operator (RLFIO) of Touchard wavelets is achieved exactly using the Hypergeometric functions. Next, by approximating the fractional derivative of the state variables and control variables using the mentioned wavelet functions, applying RLFIO, collocation method, and Gauss–Legendre quadrature formula, the considered problems are inserted into systems of algebraic equations, which can be solved using “FindRoot” package in Mathematica software. Numerical results are presented that validate the theory and show the effectiveness of the established technique.
已认证
2021年发表
- General Lagrange scaling functions: application in general model of variable order fractional partial differential equations
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variable-order
general Lagrange scaling functions
pseudo-operational matrix
partial differential equations
- 作者: Sedigheh Sabermahani, Yadollah Ordokhani, Hossein Hassani
- 发表期刊: COMPUTATIONAL & APPLIED MATHEMATICS
- 论文简介:
- This paper studies a numerical technique to solve general variable-order partial differential equations. We present a general variable-order Riemann-Liouville pseudo-operational matrix and a general variable-order fractional derivative pseudo-operational matrix for the general Lagrange scaling functions (GLSFs). These matrices are achieved generally, without considering the nodes of Lagrange polynomials. Next, by implementing the obtained pseudo-operational matrices and an optimization method, the considered problem reduces to a system of nonlinear algebraic equations. Additionally, the convergence analysis is proposed and three numerical examples illustrate its good performance.
已认证
2020年发表
- General Lagrange-hybrid functions and numerical solution of differential equations containing piecewise constant delays with bibliometric analysis
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general Lagrange-hybrid functions
piecewise constant delays
collocation method
mathematical model
- 作者: Sedigheh Sabermahani, Yadollah Ordokhani
- 发表期刊: APPLIED MATHEMATICS AND COMPUTATION
- 论文简介:
- Delay differential equations have been the topic of significant interest in scientific and engineering problems. In this manuscript, we deal with the numerical solution of delay differential equations containing piecewise constant delays. The present method is based on general Lagrange-hybrid functions (GLHFs) and collocation method. First, we define GLHFs without considering the nodes of Lagrange polynomials. The integration operational matrix and delay operational matrix of GLHFs are obtained, generally. Using the integration and delay operational matrices and collocation method, the proposed problem transforms into a system of algebraic equations. An estimation of the error is derived in the sense of the Sobolev norm. Several numerical examples are given to demonstrate the accuracy and validity of the proposed computational procedure, as the mathematical model of tumor growth in mice and HIV …