Papers by Sedigheh Sabermahani
Modified wavelets technique for multitype 2D fractional optimal control problems
Journal of vibration and control, Jun 19, 2024
Zenodo (CERN European Organization for Nuclear Research), May 11, 2022
Here, we present a numerical scheme to solve optimal control problems with time-varying delay sys... more Here, we present a numerical scheme to solve optimal control problems with time-varying delay system. This method is based on Lucas wavelets and Galerkin method. Operational matrices of integration and delay for Lucas wavelets are proposed. Then, Galerkin method is used to solve the mentioned problems. Numerical results are included to demonstrate the efficiency of the present technique.
Social Science Research Network, Jun 7, 2019
Zenodo (CERN European Organization for Nuclear Research), Feb 8, 2023
The main aim of this study is to present a computational method based on Fibonacci polynomials fo... more The main aim of this study is to present a computational method based on Fibonacci polynomials for solving fractional nonlinear optimal control problems, where this scheme is applied to solving the optimal control problems of cancer treatment. Here, a pseudo-operational matrix of fractional integration is presented for the considered polynomials. Then, we use this matrix, the Gaussian quadrature rule, and the collocation method to reduce the given problem into a system of algebraic equations. The effectiveness of the present technique is tested by means of one example and the results confirm its good performance.
Bernoulli wavelet least squares support vector regression: Robust numerical method for systems of fractional differential equations
Mathematical Methods in the Applied Sciences
In this study, a new hybrid method is developed to solve linear or nonlinear systems of fractiona... more In this study, a new hybrid method is developed to solve linear or nonlinear systems of fractional differential equations using Bernoulli wavelets (Bws) and the least squares support vector regression (LS‐SVR). The numerical methods based on operational matrices for solving various kinds of fractional equations have been widely studied in the last decade. In contrast to the existing methods, here we derive the operator of fractional integration, aiming to remove the approximation error. For this purpose, we present Bw operator of Riemann–Liouville fractional integration and use it in our scheme. In the proposed technique, we approximate the unknown functions via Bws, and then with the help of Bw operator of fractional integration and LS‐SVR, we reduce the problem to an algebraic system. In this way, we simplify the computation of the considered system. The error analysis of our method is proposed. Finally, we demonstrate the applicability of the present scheme by solving several num...
Hahn hybrid functions for solving distributed order fractional Black–Scholes European option pricing problem arising in financial market
Mathematical Methods in the Applied Sciences
The main purpose of this work is to present a new numerical method based on Hahn hybrid functions... more 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.
Zenodo (CERN European Organization for Nuclear Research), Jul 14, 2022
The principal purpose of the current work is to solve a class of time-space fractional pantograph... more The principal purpose of the current work is to solve a class of time-space fractional pantograph differential equations. We present the operational matrices of fractional integral operator and pantograph for Lucas polynomials. Then, these matrices are applied to convert the considered problem to a system of algebraic equations with unknown coefficients. Then, two examples are presented to demonstrate the effectiveness of the present method.
Hahn hybrid functions for solving distributed order fractional Black–Scholes European option pricing problem arising in financial market
Mathematical Methods in The Applied Sciences, Dec 8, 2022
The main purpose of this work is to present a new numerical method based on Hahn hybrid functions... more 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.
A numerical technique for solving fractional Benjamin–Bona–Mahony–Burgers equations with bibliometric analysis
Elsevier eBooks, 2023
Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems
Chaos, Solitons & Fractals
Fractional-Order Mittag–Leffler Functions for Solving Multi-dimensional Fractional Pantograph Delay Differential Equations
Iranian Journal of Science
Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method
Journal of Vibration and Control
A new approach to finding the approximate solution of distributed-order fractional optimal contro... more 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.
Ritz-generalized Pell wavelet method: Application for two classes of fractional pantograph problems
Communications in Nonlinear Science and Numerical Simulation
CERN European Organization for Nuclear Research - Zenodo, May 11, 2022
SSRN Electronic Journal
In this paper, we present a numerical method for pricing European options. This approximation met... more In this paper, we present a numerical method for pricing European options. This approximation method is based on the characteristic function and family of B-Spline function (including: Linear, Quadratic and Cubic B-Spline).
Solution of optimal control problems governed by volterra integral and fractional integro-differential equations
Journal of Vibration and Control
In this manuscript, we investigate two categories of optimal control problems (OCPs), OPCs via fr... more 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.
Numerical solution of a fractional epidemic model via general Lagrange scaling functions with bibliometric analysis
Mathematical Analysis of Infectious Diseases
Application of Two-Dimensional Fibonacci Wavelets in Fractional Partial Differential Equations Arising in the Financial Market
International Journal of Applied and Computational Mathematics
Touchard wavelet technique for solving time-fractional Black–Scholes model
Computational and Applied Mathematics
Bernoulli wavelet least square support vector regression: Robust numerical method for systems of fractional differential equations
In this study, a new hybrid method is developed to solve a system of linear or nonlinear fraction... more In this study, a new hybrid method is developed to solve a system of linear or nonlinear fractional differential equations using Bernoulli wavelets (Bws) and the least square support vector regression(LS-SVR). For this purpose, we present Bw operator of Riemann-Liouville fractional integration for Bw and use it in our scheme. In the proposed technique, we approximate the unknown functions via Bws, then with the help of Bw operator of fractional integration and LS-SVR, we reduce the problem to an algebraic system. In this way, we simplify the computation of the considered system. The error analysis is proposed. Finally, we demonstrate the applicability of the present scheme by solving several numerical examples.
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Papers by Sedigheh Sabermahani