An indirect spectral shifted Gegenbauer collocation method for discretizing fractional optimal control problems


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Authors

  • Mushtaq Salh Ali Department of Mathematics, Open Educational College, Ministary of Education, Al Najaf Center
  • Wisam Rafid Dawood Department of Mathematics, AL-Nahrain University, College Of Scinces Computer Science, Department of Mathematics,Bagdad,Iraq https://orcid.org/0009-0005-4223-7553
  • Dr. Mohammed K Almoaeet techer Department of Mathematics, College of Education , University of Babylon, Babylon, Iraq, https://orcid.org/0000-0002-2700-2802
  • Mohammed Jawad Al-Haidarey Department of Ecology, College of Sciences, University of Kufa,

Keywords:

Keywords: Riemann-Liouville fractional derivative, Gegenbauer polynomials, Optimal control problem

Abstract

Many best properties of the shifted Gegenbauer functions were used to obtain a new
closed formula of the left and right Riemann-Liouville fractional derivative. The new formulas
have been used to approximate the solution of the fractional optimal control problems. The
indirect spectral-shifted Gegenbauer collocation method is applied to discretizing FOCPs with a
dynamic fractional differential equation. The FOCPs were reduced to the system of algebraic
equations. Special attention is given to studying the convergence analysis and estimating an
error upper bound of the presented formulas. Illustrative numerical examples are integrated to
show the truth and applicability of this new technique.

Author Biographies

Wisam Rafid Dawood, Department of Mathematics, AL-Nahrain University, College Of Scinces Computer Science, Department of Mathematics,Bagdad,Iraq

مؤخرة. ليك. وسام رافد داود : جامعة النهرين، كلية العلوم علوم الحاسوب،
قسم الرياضيات، بغداد، العراق

Dr. Mohammed K Almoaeet, techer Department of Mathematics, College of Education , University of Babylon, Babylon, Iraq,

Teacher  Mohammed K Almoaeet: Department of Mathematics, College of Education,
University of Babylon, Babylon, Iraq, momokareem2@gmail.com

References

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Published

2024-08-13

How to Cite

Ali, M. S., Dawood, W. R., Almoaeet, M., & Al-Haidarey, M. J. (2024). An indirect spectral shifted Gegenbauer collocation method for discretizing fractional optimal control problems. Results in Nonlinear Analysis, 7(3), 177–193. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/351