Open AccessAn Indirect Spectral Collocation Method Based on Shifted Jacobi Functions for Solving Some Class of Fractional Optimal Control Problems
Author(s) -
Mushtaq salh Ali,
Mohammed K. Almoaeet,
Basim Albuohimad
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1818/1/012129
Subject(s) - mathematics , collocation (remote sensing) , class (philosophy) , orthogonal collocation , jacobi polynomials , fractional calculus , collocation method , spectral method , optimal control , algebraic equation , polynomial , nonlinear system , mathematical analysis , differential equation , orthogonal polynomials , mathematical optimization , computer science , ordinary differential equation , physics , quantum mechanics , artificial intelligence , machine learning
A new approximation formula of the Riemann-Liouville fractional derivatives is derived based on shifted classical Jacobi polynomial in spectral approximations. This formula is presented to approximate indirect solution of fractional optimal control problems (FOCPs) with a fractional differential equation as the dynamic constrain. The properties of new formula allows us to use spectral collocation method to reduce FOCPs by indirect method to a system of liner/nonlinear algebraic equations. Four test examples are presented to examine the applicability and validity of a newly purposed method.