Abstract
In this work we wish to highlight some consequences of a recent result proved in (J. Integral Equ. Appl. 29: 585–608, 2017). Particular emphasis will be given to its application on fractional variational problems of Herglotz type.
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Notes
We have never seen such type of result in the literature.
That is, (1 + x)n ≥ 1 + nx for x > − 1 and \(n\in \mathbb {N}\).
In the notation of [4] we are considering here β = α.
A function \(g : \mathbb {R}^{n}\times \mathbb {R}^{n} \to \mathbb {R}^{j}\) is said to be submersive at a point \((x_{a},x_{b})\in \mathbb {R}^{n}\times \mathbb {R}^{n}\) if its differential at this point is surjective.
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Acknowledgements
The author was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Stimulus of Scientific Employment, Individual Support-2017 Call” with reference CEECIND/00640/2017.
The author would like to thank the referees for their careful reading of the manuscript, and their corrections and suggestions which contributed to improve this article.
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Ferreira, R.A.C. Sign of the Solutions of Linear Fractional Differential Equations and Some Applications. Vietnam J. Math. 51, 451–461 (2023). https://doi.org/10.1007/s10013-021-00541-4
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DOI: https://doi.org/10.1007/s10013-021-00541-4