Numerical solution for 2D-VOFOCPs by Ritz method and Gegenbauer Operational Matrix
Keywords:
Caputo fractional derivative, Operational matrix, Shifted Gegenbauer polynomials, Two-dimensional fractional optimal control, Shifted Gegenbauer polynomials.Abstract
This research introduces a Ritz method to address two-dimensional variable-order fractional optimal control problems 2D-VOFOCPs
with nonlinear dynamical system. The dynamic system under consider-
ation incorporates variable-order fractional derivatives described by the
the Caputo type has been considered, a widely recognized and essen-
tial type of fractional derivative. To implement the proposed method,
shifted Gegenbauer polynomials are employed as orthogonal basis func-
tions to approximate the control and state functions. By substituting
these approximations into the objective functional and the dynamical
system, a system of algebraic equations is derived. Solving this system
yields a solution to the 2D-VOFOCP.
The convergence analysis of the proposed method is rigorously inves-
tigated. Additionally, two numerical cases are offered to demonstrate
the efficacy and precision of the technique.
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