A new numerical Bernoulli polynomial method for solving fractional optimal control problems with vector components
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
View: 146
This Paper With 21 Page And PDF Format Ready To Download
- Certificate
- من نویسنده این مقاله هستم
استخراج به نرم افزارهای پژوهشی:
شناسه ملی سند علمی:
JR_CMDE-9-2_009
تاریخ نمایه سازی: 15 بهمن 1401
Abstract:
In this paper, a numerical method is developed and analyzed for solving a class of fractional optimal control problems (FOCPs) with vector state and control functions using polynomial approximation. The fractional derivative is considered in the Caputo sense. To implement the proposed numerical procedure, the Ritz spectral method with Bernoulli polynomials basis is applied. By applying the Bernoulli polynomials and using the numerical estimation of the unknown functions, the FOCP is reduced to solve a system of algebraic equations. By rigorous proofs, the convergence of the numerical method is derived for the given FOCP. Moreover, a new fractional operational matrix compatible with the proposed spectral method is formed to ease the complexity in the numerical computations. At last, several test problems are provided to show the applicability and effectiveness of the proposed scheme numerically.
Keywords:
Authors
Vahid Taherpour
Department of Mathematics, Khorram Abad Branch, Islamic Azad University, Khorram Abad, Iran
Mojtaba Nazari
Department of Mathematics, Khorram Abad Branch, Islamic Azad University, Khorram Abad, Iran
Ali Nemati
Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran