An efficient numerical scheme based on the shifted orthonormal Jacobi polynomials for solving fractional optimal control problems

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• 作者：Eid H Doha (1)
  Ali H Bhrawy (2) (3)
  Dumitru Baleanu (4) (5)
  Samer S Ezz-Eldien (6)
  Ramy M Hafez (6)
  
  1. Department of Mathematics ; Faculty of Science ; Cairo University ; Giza ; Egypt
  2. Department of Mathematics ; Faculty of Science ; King Abdulaziz University ; Jeddah ; Saudi Arabia
  3. Department of Mathematics ; Faculty of Science ; Beni-Suef University ; Beni-Suef ; Egypt
  4. Department of Mathematics and Computer Sciences ; Cankaya University ; Eskisehir Yolu 29.km ; Ankara ; 06810 ; Turkey
  5. Institute of Space Sciences ; Magurele-Bucharest ; 76900 ; Romania
  6. Department of Basic Science ; Institute of Information Technology ; Modern Academy ; Cairo ; Egypt
  
• 关键词：fractional optimal control problem ; Jacobi polynomials ; operational matrix ; Gauss quadrature ; Rayleigh ; Ritz method
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,135 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this article, we introduce a numerical technique for solving a general form of the fractional optimal control problem. Fractional derivatives are described in the Caputo sense. Using the properties of the shifted Jacobi orthonormal polynomials together with the operational matrix of fractional integrals (described in the Riemann-Liouville sense), we transform the fractional optimal control problem into an equivalent variational problem that can be reduced to a problem consisting of solving a system of algebraic equations by using the Legendre-Gauss quadrature formula with the Rayleigh-Ritz method. This system can be solved by any standard iteration method. For confirming the efficiency and accuracy of the proposed scheme, we introduce some numerical examples with their approximate solutions and compare our results with those achieved using other methods.