Matches in SemOpenAlex for { <https://semopenalex.org/work/W3186303640> ?p ?o ?g. }
- W3186303640 endingPage "708" @default.
- W3186303640 startingPage "672" @default.
- W3186303640 abstract "The present work was primarily motivated by our findings in the literature of some flaws within the proof of the second-order Legendre necessary optimality condition for fractional calculus of variations problems. Therefore, we were eager to elaborate a correct proof and it turns out that this goal is highly nontrivial, especially when considering final constraints. This paper is the result of our reflections on this subject. Precisely, we consider here a constrained minimization problem of a general Bolza functional that depends on a Caputo fractional derivative of order $$0 < alpha le 1$$ and on a Riemann–Liouville fractional integral of order $$beta > 0$$ , the constraint set describing general mixed initial/final constraints. The main contribution of our work is to derive corresponding first- and second-order necessary optimality conditions, namely the Euler–Lagrange equation, the transversality conditions and, of course, the Legendre condition. A detailed discussion is provided on the obstructions encountered with the classical strategy, while the new proof that we propose here is based on the Ekeland variational principle. Furthermore, we underline that some subsidiary contributions are provided all along the paper. In particular, we prove an independent and intrinsic result of fractional calculus stating that it does not exist a nontrivial function which is, together with its Caputo fractional derivative of order $$0< alpha <1$$ , compactly supported. Moreover, we also discuss some evidences claiming that Riemann–Liouville fractional integrals should be considered in the formulation of fractional calculus of variations problems in order to preserve the existence of solutions." @default.
- W3186303640 created "2021-08-02" @default.
- W3186303640 creator A5023291598 @default.
- W3186303640 creator A5086075252 @default.
- W3186303640 date "2021-07-19" @default.
- W3186303640 modified "2023-10-06" @default.
- W3186303640 title "Legendre’s Necessary Condition for Fractional Bolza Functionals with Mixed Initial/Final Constraints" @default.
- W3186303640 cites W1545761024 @default.
- W3186303640 cites W1595765050 @default.
- W3186303640 cites W185370091 @default.
- W3186303640 cites W1963577778 @default.
- W3186303640 cites W1965504976 @default.
- W3186303640 cites W1977750299 @default.
- W3186303640 cites W1991199035 @default.
- W3186303640 cites W1999508879 @default.
- W3186303640 cites W2001326020 @default.
- W3186303640 cites W2015882123 @default.
- W3186303640 cites W2023998685 @default.
- W3186303640 cites W2024025366 @default.
- W3186303640 cites W2045176173 @default.
- W3186303640 cites W2055701161 @default.
- W3186303640 cites W2055958036 @default.
- W3186303640 cites W2058411932 @default.
- W3186303640 cites W2062163287 @default.
- W3186303640 cites W2063133641 @default.
- W3186303640 cites W2064361774 @default.
- W3186303640 cites W2076005793 @default.
- W3186303640 cites W2080002959 @default.
- W3186303640 cites W2081440761 @default.
- W3186303640 cites W2083118792 @default.
- W3186303640 cites W2084795903 @default.
- W3186303640 cites W2088589842 @default.
- W3186303640 cites W2094706142 @default.
- W3186303640 cites W2102326085 @default.
- W3186303640 cites W2105373440 @default.
- W3186303640 cites W2105487017 @default.
- W3186303640 cites W2111271983 @default.
- W3186303640 cites W2132978934 @default.
- W3186303640 cites W2141961077 @default.
- W3186303640 cites W2149296108 @default.
- W3186303640 cites W2293396668 @default.
- W3186303640 cites W2346941360 @default.
- W3186303640 cites W2476716509 @default.
- W3186303640 cites W2480459371 @default.
- W3186303640 cites W2506586217 @default.
- W3186303640 cites W2541668934 @default.
- W3186303640 cites W2808000091 @default.
- W3186303640 cites W2909538096 @default.
- W3186303640 cites W2964261594 @default.
- W3186303640 cites W2982271919 @default.
- W3186303640 cites W3099055406 @default.
- W3186303640 cites W3099677191 @default.
- W3186303640 cites W3100222141 @default.
- W3186303640 cites W3102894372 @default.
- W3186303640 cites W3106382556 @default.
- W3186303640 cites W4253856151 @default.
- W3186303640 cites W4292402580 @default.
- W3186303640 cites W4301223505 @default.
- W3186303640 cites W4301747304 @default.
- W3186303640 doi "https://doi.org/10.1007/s10957-021-01908-w" @default.
- W3186303640 hasPublicationYear "2021" @default.
- W3186303640 type Work @default.
- W3186303640 sameAs 3186303640 @default.
- W3186303640 citedByCount "1" @default.
- W3186303640 countsByYear W31863036402023 @default.
- W3186303640 crossrefType "journal-article" @default.
- W3186303640 hasAuthorship W3186303640A5023291598 @default.
- W3186303640 hasAuthorship W3186303640A5086075252 @default.
- W3186303640 hasBestOaLocation W31863036402 @default.
- W3186303640 hasConcept C10138342 @default.
- W3186303640 hasConcept C111458787 @default.
- W3186303640 hasConcept C134306372 @default.
- W3186303640 hasConcept C153262748 @default.
- W3186303640 hasConcept C154249771 @default.
- W3186303640 hasConcept C162324750 @default.
- W3186303640 hasConcept C182306322 @default.
- W3186303640 hasConcept C24167531 @default.
- W3186303640 hasConcept C2776392105 @default.
- W3186303640 hasConcept C28826006 @default.
- W3186303640 hasConcept C33923547 @default.
- W3186303640 hasConcept C53469067 @default.
- W3186303640 hasConcept C97985569 @default.
- W3186303640 hasConceptScore W3186303640C10138342 @default.
- W3186303640 hasConceptScore W3186303640C111458787 @default.
- W3186303640 hasConceptScore W3186303640C134306372 @default.
- W3186303640 hasConceptScore W3186303640C153262748 @default.
- W3186303640 hasConceptScore W3186303640C154249771 @default.
- W3186303640 hasConceptScore W3186303640C162324750 @default.
- W3186303640 hasConceptScore W3186303640C182306322 @default.
- W3186303640 hasConceptScore W3186303640C24167531 @default.
- W3186303640 hasConceptScore W3186303640C2776392105 @default.
- W3186303640 hasConceptScore W3186303640C28826006 @default.
- W3186303640 hasConceptScore W3186303640C33923547 @default.
- W3186303640 hasConceptScore W3186303640C53469067 @default.
- W3186303640 hasConceptScore W3186303640C97985569 @default.
- W3186303640 hasFunder F4320334779 @default.
- W3186303640 hasIssue "2" @default.
- W3186303640 hasLocation W31863036401 @default.