Minimization Problems for Functionals Depending on Generalized Proportional Fractional Derivatives

In this work we study variational problems, where ordinary derivatives are replaced by a generalized proportional fractional derivative. This fractional operator depends on a fixed parameter, acting as a weight over the state function and its first-order derivative. We consider the problem with and...

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Bibliographic Details
Published in:Fractal and fractional 2022-07, Vol.6 (7), p.356
Main Author: Almeida, Ricardo
Format: Article
Language:English
Subjects:
Boundary conditions
Calculus
Calculus of variations
fractional calculus
generalized proportional fractional
Mathematical functions
Operators (mathematics)
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Summary:In this work we study variational problems, where ordinary derivatives are replaced by a generalized proportional fractional derivative. This fractional operator depends on a fixed parameter, acting as a weight over the state function and its first-order derivative. We consider the problem with and without boundary conditions, and with additional restrictions like isoperimetric and holonomic. Herglotz’s variational problem and when in presence of time delays are also considered.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract6070356