A Numerical Study for Solving Fractional-Order Systems of Optimal Control Using B-Cubic Spline

Oday  Al-Shaher; M Mahmoudi; Mohammed Sahib Mechee

doi:10.30526/38.2.3665

Authors

Oday Al-Shaher Department of Mathematics, University of Qom, Qom, Iran https://orcid.org/0000-0001-5129-1619
M Mahmoudi Department of Mathematics, University of Qom, Qom, Iran https://orcid.org/0000-0002-1607-9329
Mohammed Sahib Mechee Information Technology Research and Development Centre, University of Kufa, Najaf, Iraq. https://orcid.org/0000-0002-6522-1811

DOI:

https://doi.org/10.30526/38.2.3665

Keywords:

Quasi-linear, Fractional Differential Equations; Spline; Collection; DEs; ODEs, FDEs

Abstract

Using B-cubic spline base, the numerical solutions of optimal control of dynamical systems of fractional-order have been examined. In order to determine the dynamical system's control function through time whilst optimizing an objective optimal function. There are numerous applications for the optimal control system in science, engineering and the one branch of applied mathematics operations research. The primary goal of this study is to approximate the numerical solutions for a fractional-order optimal control systems in both free and non-free terminal time (TT). The collocation approach considers a numerical solution to this problem by using a B-cubic spline base. A numerical comparison has been introduced between the analytical solutions with numerical solutions using the proposed method. Exemplifications of implementations using various computer simulations revealed that the proposed method is both accurate and efficient.

Author Biographies

Oday Al-Shaher, Department of Mathematics, University of Qom, Qom, Iran

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M Mahmoudi, Department of Mathematics, University of Qom, Qom, Iran

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Mohammed Sahib Mechee, Information Technology Research and Development Centre, University of Kufa, Najaf, Iraq.

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