Sedigheh Sabermahani's profile, Alzahra University

Sedigheh Sabermahani

Iran Alzahra University

19 Papers

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Research field: Numerical Analysis, Computational method, Optimal control problems, Delay system, Wavelet

Bio: Sedigheh Sabermahani received her MSc in Applied Mathematics from the Shahid Beheshti University of Tehran (2011-2013). She completed her Ph.D. in Applied Mathematics from the Alzahra University of Te... More

Position: Postdoctoral Researcher

Personal page: https://www.researchgate.net/profile/Sedigheh-Sabermahani

LinkedIn: https://www.linkedin.com/in/sedigheh-sabermahani-14986b184/

ORCID: 0000-0002-7320-8908

Address: Alzahra university, Tehran, Iran

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ORCID

Published in 2023

Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems: fractional optimal control problems Atangana–Riemann–Liouville derivative Ritz method pseudo-operational matrix; Authors: Sedigheh Sabermahani, Yadollah Ordokhani, Parisa Rahimkhani; Journal: Chaos, Solitons & Fractals

Description:: 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

Published in 2023

Fractional-Order Mittag–Leffler Functions for Solving Multi-dimensional Fractional Pantograph Delay Differential Equations: fractional-order Mittag–Leffler functions pantograph differential equation pseudo-operational matrix collocation method; Authors: Arezoo Ghasempour, Yadollah Ordokhani, Sedigheh Sabermahani; Journal: Iranian Journal of Science

Description:: 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.

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Published in 2023

Hahn hybrid functions for solving distributed order fractional Black–Scholes European option pricing problem arising in financial market: hybrid functions distributed order Gauss–Legendre quadrature formula Black–Scholes option pricing; Authors: Parisa Rahimkhani, Yadollah Ordokhani, Sedigheh Sabermahani; Journal: Mathematical Methods in the Applied Sciences

Description:: 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

Published in 2023

Ritz-generalized Pell wavelet method: Application for two classes of fractional pantograph problems: wavelets pantograph differential equations optimal control problems Ritz and collocation methods; Authors: Sedigheh Sabermahani, Yadollah Ordokhani, Mohsen Razzaghi; Journal: Communications in Nonlinear Science and Numerical Simulation

Description:: 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

Published in 2023

Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method: distributed-order optimal control problems operational matrix wavelets; Authors: Sedigheh Sabermahani, Yadollah Ordokhani; Journal: Journal of Vibration and Control

Description:: 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.

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Published in 2022

Touchard wavelet technique for solving time-fractional Black–Scholes model: time-fractional Black–Scholes equations wavelets pseudo-operational matrix numerical method; Authors: Farshid Nourian, Mehrdad Lakestani, Sedigheh Sabermahani, Yadollah Ordokhani; Journal: COMPUTATIONAL & APPLIED MATHEMATICS

Description:: 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.

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Published in 2022

Application of Two-Dimensional Fibonacci Wavelets in Fractional Partial Differential Equations Arising in the Financial Market: wavelets fractional Black–Scholes equations Riemann–Liouville pseudo-operational matrix bibliometric analysis; Authors: Sedigheh Sabermahani, Yadollah Ordokhani, Parisa Rahimkhani; Journal: International Journal of Applied and Computational Mathematics

Description:: 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 …

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Published in 2022

Solution of optimal control problems governed by volterra integral and fractional integro-differential equations: wavelets optimal control problems fractional Volterra integro-differential equations Volterra integral equations; Authors: Sedigheh Sabermahani, Yadollah Ordokhani, Kobra Rabiei, Mohsen Razzaghi; Journal: Journal of Vibration and Control

Description:: 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.

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Published in 2021

General Lagrange scaling functions: application in general model of variable order fractional partial differential equations: variable-order general Lagrange scaling functions pseudo-operational matrix partial differential equations; Authors: Sedigheh Sabermahani, Yadollah Ordokhani, Hossein Hassani; Journal: COMPUTATIONAL & APPLIED MATHEMATICS

Description:: 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.

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Published in 2020

General Lagrange-hybrid functions and numerical solution of differential equations containing piecewise constant delays with bibliometric analysis: general Lagrange-hybrid functions piecewise constant delays collocation method mathematical model; Authors: Sedigheh Sabermahani, Yadollah Ordokhani; Journal: APPLIED MATHEMATICS AND COMPUTATION

Description:: 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 …