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Title: Boubaker hybrid functions and their application to solve fractional optimal control and fractional variational problems (English)
Author: Rabiei, Kobra
Author: Ordokhani, Yadollah
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 63
Issue: 5
Year: 2018
Pages: 541-567
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: fractional optimal control problems
Keyword: fractional variational problems
Keyword: Riemann-Liouville fractional integration
Keyword: hybrid functions
Keyword: Boubaker polynomials
Keyword: Laplace transform
Keyword: convergence analysis
MSC: 49J15
MSC: 49J40
idZBL: Zbl 06986925
idMR: MR3870148
DOI: 10.21136/AM.2018.0083-18
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Date available: 2018-10-23T06:58:27Z
Last updated: 2020-11-02
Stable URL: http://hdl.handle.net/10338.dmlcz/147413
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