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dc.contributor.authorKamocki, Rafał
dc.date.accessioned2015-10-28T12:44:44Z
dc.date.available2015-10-28T12:44:44Z
dc.date.issued2015-07-08
dc.identifier.issn1563-5147
dc.identifier.urihttp://hdl.handle.net/11089/12946
dc.description.abstractWe investigate a fractional Dirichlet problem involving Jumarie’s derivative. Using some variational methods a theorem on the existence and uniqueness of a solution to such problem is proved. In the proof of the main result we use a fractional counterpart of the du Bois-Reymond fundamental lemma.pl_PL
dc.description.sponsorshipThe project was financially supported by the Faculty of Mathematics and Computer Science, University of Lodz, under Grant no. B1411600000451.02 for young researchers and participants of a grad school.pl_PL
dc.language.isoenpl_PL
dc.publisherHindawi Publishing Corporationpl_PL
dc.relation.ispartofseriesMathematical Problems in Engineering;
dc.rightsUznanie autorstwa 3.0 Polska*
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/pl/*
dc.titleVariational Methods for a Fractional Dirichlet Problem Involving Jumarie’s Derivativepl_PL
dc.typeArticlepl_PL
dc.page.number1-9pl_PL
dc.contributor.authorAffiliationKamocki Rafał, Faculty of Mathematics and Computer Science, University of Lodzpl_PL
dc.referencesA. Carpinteri and F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics, Springer, Berlin, Germany, 1997.pl_PL
dc.referencesR. Hilfer, Applications of Fractional Calculus in Physics, World Scientific Publishing, River Edge, NJ, USA, 2000.pl_PL
dc.referencesA. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006.pl_PL
dc.referencesS. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives and Some Their Applications, Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993.pl_PL
dc.referencesB. J.West and P. Grigolini, Applications of Fractional Calculus in Physics,World Scientific, Singapore, 1998.pl_PL
dc.referencesB. Ross, S. G. Samko, and E. R. Love, “Functions that have no first order derivative might have fractional derivatives of all orders less than one,” Real Analysis Exchange, vol. 20, no. 1, pp. 140–157, 1994-1995.pl_PL
dc.referencesG. Jumarie, “Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations,” Insurance: Mathematics&Economics, vol. 42,no. 1, pp. 271–287, 2008.pl_PL
dc.referencesG. Jumarie, “On the representation of fractional Brownian motion as an integral with respect to (d),” AppliedMathematics Letters, vol. 18, no. 7, pp. 739–748, 2005.pl_PL
dc.referencesG. Jumarie, “Table of some basic fractional calculus formulae derived froma modified Riemann-Liouville derivative for nondifferentiable functions,” Applied Mathematics Letters, vol. 22, no. 3, pp. 378–385, 2009.pl_PL
dc.referencesG. Jumarie, FractionalDifferential Calculus forNondifferentiable Functions, LAP Lambert Academic Publishing, 2013.pl_PL
dc.referencesJ. Mawhin, Problemes de Dirichlet Variationnels Non-Lin´eaires, vol. 104, Les Presses de L’Universit´e de Montr´eal, Montreal, Canada, 1987pl_PL
dc.referencesR. Kamocki and M. Majewski, “On a fractional Dirichlet problem,” in Proceedings of the 17th International Conference on Methods andModels in Automation&Robotics (MMAR ’12), pp. 60–63, Miedzyzdrojie, Poland, August 2012.pl_PL
dc.referencesA. B. Malinowska and D. F. M. Torres, Introduction to the Fractional Calculus of Variations, Imperial College Press, London, UK, 2012.pl_PL
dc.referencesR. Kamocki, “Pontryagin maximum principle for fractional ordinary optimal control problems,” Mathematical Methods in the Applied Sciences, vol. 37, no. 11, pp. 1668–1686, 2014.pl_PL
dc.referencesL. Bourdin, “Existence of a weak solution for fractional Euler- Lagrange equations,” Journal of Mathematical Analysis and Applications, vol. 399, no. 1, pp. 239–251, 2013.pl_PL
dc.referencesM. J. Lazo and D. F. Torres, “The DuBois-Reymond fundamental lemma of the fractional calculus of variations and an Euler-Lagrange equation involving only derivatives of Caputo,” Journal of OptimizationTheory and Applications, vol. 156, no. 1, pp. 56–67, 2013.pl_PL
dc.referencesV. M. Alekse’ev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control, Fizmatlit, Moscow, Russia, 2005, (Russian).pl_PL
dc.contributor.authorEmailrafkam@math.uni.lodz.plpl_PL
dc.identifier.doihttp://dx.doi.org/10.1155/2015/248517
dc.relation.volumeVolume 2015pl_PL


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