TY - JOUR
ID - 15277
TI - Numerical method for solving a class of two-dimensional fractional optimal control problem of via operational matrices of Legendre polynomial
JO - Journal of Advanced Mathematical Modeling
JA - JAMM
LA - en
SN - 2251-8088
AU - nouralizade, yaser
AU - Behroozifar, Mahmoud
AU - Alipour, Mohsen
AD - Department of Mathematics, Babol Noshirvani university of tecgnology, Babol, Iran
Y1 - 2020
PY - 2020
VL - 10
IS - 1
SP - 1
EP - 18
KW - Partial differential of fractional Caputo
KW - Legendre polynomial
KW - Operational matrices
KW - Legendre-Gauss integration rule
DO - 10.22055/jamm.2020.24146.1516
N2 - In this article, we present a numerical method for solving a class of two-dimensional fractional optimal control problems by the Legendre polynomial basis with fractional operational matrix. It should be mentioned that the dynamic system of the problem is based on the Caputo fractional partial derivative. This method, the dual integral is approximated by Gauss-Legendre rule, and then by using the Lagrangian equation, a nonlinear equation is obtained. This nonlinear equation set is solved by Newton's iterative method and unknown coefficients is determined. Finally, the proposed method was applied on a fractional problem with the different degree of fractional derivative. Also, the CPU time of method is exhibited. It is notable that all calculations were obtained by the Mathematica software.
UR - https://jamm.scu.ac.ir/article_15277.html
L1 - https://jamm.scu.ac.ir/article_15277_d4f8d53583a73342f0fdd4301316789f.pdf
ER -