Browsing by Author "Mohammadi, F."

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Citation Count: Moradi, L.; Mohammadi, F.; Baleanu, D., "A direct numerical solution of time-delay fractional optimal control problems by using Chelyshkov wavelets", Journal of Vibration and Control, Vol. 25, No. 2, pp. 310-324, (2019).
A direct numerical solution of time-delay fractional optimal control problems by using Chelyshkov wavelets
(Sage Publications LTD, 2019) Moradi, L.; Mohammadi, F.; Baleanu, Dumitru; 56389
The aim of the present study is to present a numerical algorithm for solving time-delay fractional optimal control problems (TDFOCPs). First, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet functions and their properties are implemented to derive some operational matrices. Then, the fractional derivative of the state function in the dynamic constraint of TDFOCPs is approximated by means of the Chelyshkov wavelets. The operational matrix of fractional integration together with the dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the performance index and necessary conditions for optimality transform the under consideration TDFOCPs into an algebraic system. Moreover, some illustrative examples are considered and the obtained numerical results were compared with those previously published in the literature.
Citation Count: Azin, H.; Mohammadi, F.; Baleanu, Dumitru (2020). "A Generalized Barycentric Rational Interpolation Method for Generalized Abel Integral Equations", International Journal of Applied and Computational Mathematics, Vol. 6, No. 5.
A Generalized Barycentric Rational Interpolation Method for Generalized Abel Integral Equations
(2020) Azin, H.; Mohammadi, F.; Baleanu, Dumitru; 56389
The paper is devoted to the numerical solution of generalized Abel integral equation. First, the generalized barycentric rational interpolants have been introduced and their properties investigated thoroughly. Then, a numerical method based on these barycentric rational interpolations and the Legendre–Gauss quadrature rule is developed for solving the generalized Abel integral equation. The main advantages of the presented method is that it provides an infinitely smooth approximate solution with no real poles for the generalized Abel integral equation. © 2020, Springer Nature India Private Limited.
Citation Count: Mohammadi, F.; Moradi, L.; Baleanu, D. "A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems", Journal of Vibration and Control, Vol. 24, No. 21. pp. 5030-5043, (2018).
A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems
(Sage Publications LTD, 2018) Mohammadi, F.; Moradi, L.; Baleanu, Dumitru; Jajarmi, Amin; 56389
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.