Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems

Kobra Rabiei; Yadollah Ordokhani

Applications of Mathematics (2018)

  • Volume: 63, Issue: 5, page 541-567
  • ISSN: 0862-7940

Abstract

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A new hybrid of block-pulse functions and Boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems (FOCPs) with quadratic performance index and fractional variational problems (FVPs). First, the general formulation of the Riemann-Liouville integral operator for Boubaker hybrid function is presented for the first time. Then it is applied to reduce the problems to optimization problems, which can be solved by the existing method. In this way we find the extremum value of FOCPs without adding slack variables to inequality trajectories. Also we show that if the number of bases is increased, the used approximations in this method are convergent. The applicability and validity of the method are shown by numerical results of some examples, moreover, a comparison with the existing results shows the preference of this method.

How to cite

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Rabiei, Kobra, and Ordokhani, Yadollah. "Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems." Applications of Mathematics 63.5 (2018): 541-567. <http://eudml.org/doc/294816>.

@article{Rabiei2018,
abstract = {A new hybrid of block-pulse functions and Boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems (FOCPs) with quadratic performance index and fractional variational problems (FVPs). First, the general formulation of the Riemann-Liouville integral operator for Boubaker hybrid function is presented for the first time. Then it is applied to reduce the problems to optimization problems, which can be solved by the existing method. In this way we find the extremum value of FOCPs without adding slack variables to inequality trajectories. Also we show that if the number of bases is increased, the used approximations in this method are convergent. The applicability and validity of the method are shown by numerical results of some examples, moreover, a comparison with the existing results shows the preference of this method.},
author = {Rabiei, Kobra, Ordokhani, Yadollah},
journal = {Applications of Mathematics},
keywords = {fractional optimal control problems; fractional variational problems; Riemann-Liouville fractional integration; hybrid functions; Boubaker polynomials; Laplace transform; convergence analysis},
language = {eng},
number = {5},
pages = {541-567},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems},
url = {http://eudml.org/doc/294816},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Rabiei, Kobra
AU - Ordokhani, Yadollah
TI - Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 5
SP - 541
EP - 567
AB - A new hybrid of block-pulse functions and Boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems (FOCPs) with quadratic performance index and fractional variational problems (FVPs). First, the general formulation of the Riemann-Liouville integral operator for Boubaker hybrid function is presented for the first time. Then it is applied to reduce the problems to optimization problems, which can be solved by the existing method. In this way we find the extremum value of FOCPs without adding slack variables to inequality trajectories. Also we show that if the number of bases is increased, the used approximations in this method are convergent. The applicability and validity of the method are shown by numerical results of some examples, moreover, a comparison with the existing results shows the preference of this method.
LA - eng
KW - fractional optimal control problems; fractional variational problems; Riemann-Liouville fractional integration; hybrid functions; Boubaker polynomials; Laplace transform; convergence analysis
UR - http://eudml.org/doc/294816
ER -

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