Orthonormal piecewise Bernoulli functions: Application for optimal control problems generated using fractional integro-differential equations
Keyword(s):
In this study, the orthonormal piecewise Bernoulli functions are generated as a new kind of basis functions. An explicit matrix related to fractional integration of these functions is obtained. An efficient direct method is developed to solve a novel set of optimal control problems defined using a fractional integro-differential equation. The presented technique is based on the expressed basis functions and their fractional integral matrix together with the Gauss–Legendre integration method and the Lagrange multipliers algorithm. This approach converts the original problem into a mathematical programming one. Three examples are investigated numerically to verify the capability and reliability of the approach.
2019 ◽
Vol 356
(15)
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pp. 8216-8236
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2002 ◽
Vol 35
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pp. 479-484
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2013 ◽
Vol 20
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pp. 1394-1416
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2018 ◽
Vol 25
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pp. 1080-1095
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2019 ◽
Vol 39
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1991 ◽
Vol 159
(1)
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pp. 295-314
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2018 ◽
Vol 355
(12)
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pp. 4970-4995
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