dc.contributor.author | Kamocki, Rafał | |
dc.date.accessioned | 2015-10-28T12:44:44Z | |
dc.date.available | 2015-10-28T12:44:44Z | |
dc.date.issued | 2015-07-08 | |
dc.identifier.issn | 1563-5147 | |
dc.identifier.uri | http://hdl.handle.net/11089/12946 | |
dc.description.abstract | We 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.sponsorship | The 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.iso | en | pl_PL |
dc.publisher | Hindawi Publishing Corporation | pl_PL |
dc.relation.ispartofseries | Mathematical Problems in Engineering; | |
dc.rights | Uznanie autorstwa 3.0 Polska | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/pl/ | * |
dc.title | Variational Methods for a Fractional Dirichlet Problem Involving Jumarie’s Derivative | pl_PL |
dc.type | Article | pl_PL |
dc.page.number | 1-9 | pl_PL |
dc.contributor.authorAffiliation | Kamocki Rafał, Faculty of Mathematics and Computer Science, University of Lodz | pl_PL |
dc.references | A. Carpinteri and F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics, Springer, Berlin, Germany, 1997. | pl_PL |
dc.references | R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific Publishing, River Edge, NJ, USA, 2000. | pl_PL |
dc.references | A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006. | pl_PL |
dc.references | S. 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.references | B. J.West and P. Grigolini, Applications of Fractional Calculus in Physics,World Scientific, Singapore, 1998. | pl_PL |
dc.references | B. 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.references | G. 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.references | G. 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.references | G. 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.references | G. Jumarie, FractionalDifferential Calculus forNondifferentiable Functions, LAP Lambert Academic Publishing, 2013. | pl_PL |
dc.references | J. Mawhin, Problemes de Dirichlet Variationnels Non-Lin´eaires, vol. 104, Les Presses de L’Universit´e de Montr´eal, Montreal, Canada, 1987 | pl_PL |
dc.references | R. 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.references | A. B. Malinowska and D. F. M. Torres, Introduction to the Fractional Calculus of Variations, Imperial College Press, London, UK, 2012. | pl_PL |
dc.references | R. 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.references | L. 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.references | M. 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.references | V. M. Alekse’ev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control, Fizmatlit, Moscow, Russia, 2005, (Russian). | pl_PL |
dc.contributor.authorEmail | rafkam@math.uni.lodz.pl | pl_PL |
dc.identifier.doi | http://dx.doi.org/10.1155/2015/248517 | |
dc.relation.volume | Volume 2015 | pl_PL |