Title : ( An efficient approximate method for solving two-dimensional fractional optimal control problems using generalized fractional order of Bernstein functions )
Authors: ali ketabdari , Mohammad Hadi Farahi , Sohrab Effati ,
Full TextAbstract
We define a new operational matrix of fractional derivative in the Caputo type and apply a spectral method to solve a two-dimensional fractional optimal control problem (2D-FOCP). To acquire this aim, first we expand the state and control variables based on the fractional order of Bernstein functions. Then we reduce the constraints of 2D-FOCP to a system of algebraic equations through the operational matrix. Now, one can solve straightforward the problem and drive the approximate solution of state and control variables. The convergence of the method in approximating the 2D-FOCP is proved. We demonstrate the efficiency and superiority of the method by comparing the results obtained by the presented method with the results of previous methods in some examples.
Keywords
fractional optimal control problems; fractional power Bernstein functions; operational matrix; Caputo derivative
@article{paperid:1082666,
author = {Ketabdari, Ali and Farahi, Mohammad Hadi and Effati, Sohrab},
title = {An efficient approximate method for solving two-dimensional fractional optimal control problems using generalized fractional order of Bernstein functions},
journal = {IMA Journal of Mathematical Control and Information},
year = {2020},
volume = {38},
number = {1},
month = {December},
issn = {0265-0754},
pages = {378--395},
numpages = {17},
keywords = {fractional optimal control problems; fractional power Bernstein functions; operational matrix;
Caputo derivative},
}
%0 Journal Article
%T An efficient approximate method for solving two-dimensional fractional optimal control problems using generalized fractional order of Bernstein functions
%A Ketabdari, Ali
%A Farahi, Mohammad Hadi
%A Effati, Sohrab
%J IMA Journal of Mathematical Control and Information
%@ 0265-0754
%D 2020
