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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 871912, 24 pages
Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
1Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
2Faculty of Computer Science, Białystok University of Technology, 15-351 Białystok, Poland
Received 1 January 2012; Revised 25 February 2012; Accepted 27 February 2012
Academic Editor: Muhammad Aslam Noor
Copyright © 2012 Tatiana Odzijewicz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [18 citations]
The following is the list of published articles that have cited the current article.
- Matheus J. Lazo, and Delfim F. M. Torres, “The DuBois–Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler–Lagrange Equation Involving Only Derivatives of Caputo,” Journal of Optimization Theory and Applications, vol. 156, no. 1, pp. 56–67, 2012.
- A. B. Malinowska, and D. F. M. Torres, “Fractional calculus of variations of several independent variables,” European Physical Journal-Special Topics, vol. 222, no. 8, pp. 1813–1826, 2013.
- Rami Ahmad El-Nabulsi, “Non-standard fractional Lagrangians,” Nonlinear Dynamics, 2013.
- A. R. El-Nabulsi, “Modified Proca equation and modified dispersion relation from a power-law Lagrangian functional,” Indian Journal Of Physics, vol. 87, no. 5, pp. 465–470, 2013.
- Dongling Wang, and Aiguo Xiao, “Numerical Methods for Fractional Variational Problems Depending on Indefinite Integrals,” Journal of Computational and Nonlinear Dynamics, vol. 8, no. 2, 2013.
- Loïc 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.
- Tatiana Odzijewicz, Agnieszka B. Malinowska, and Delfim F. M. Torres, “Green's theorem for generalized fractional derivatives,” Fractional Calculus and Applied Analysis, vol. 16, no. 1, pp. 64–75, 2013.
- Shakoor Pooseh, Ricardo Almeida, and Delfim F.M. Torres, “Discrete direct methods in the fractional calculus of variations,” Computers & Mathematics with Applications, 2013.
- Giorgio S. Taverna, and Delfim F.M. Torres, “Generalized fractional operators for nonstandard Lagrangians,” Mathematical Methods in the Applied Sciences, 2014.
- Loic Bourdin, Tatiana Odzijewicz, and Delfim F. M. Torres, “Existence Of Minimizers For Generalized Lagrangian Functionals And A Necessary Optimality Condition - Application To Fractional Variational Problems,” Differential and Integral Equations, vol. 27, no. 7-8, pp. 743–766, 2014.
- Rami Ahmad El-Nabulsi, “Fractional variational symmetries of Lagrangians, the fractional Galilean transformation and the modified Schrodinger equation,” Nonlinear Dynamics, vol. 81, no. 1-2, pp. 939–948, 2015.
- Ricardo Almeida, and Natalia Martins, “Variational problems for Holderian functions with free terminal point,” Mathematical Methods In The Applied Sciences, vol. 38, no. 6, pp. 1059–1069, 2015.
- Rajesh K. Pandey, and Om P. Agrawal, “Numerical Scheme for a Quadratic Type Generalized Isoperimetric Constraint Variational Problems With A-Operator,” Journal Of Computational And Nonlinear Dynamics, vol. 10, no. 2, 2015.
- Udita N. Katugampola, “Mellin transforms of generalized fractional integrals and derivatives,” Applied Mathematics and Computation, 2015.
- Mohammad Maleki, Ishak Hashim, Saeid Abbasbandy, and A. Alsaedi, “Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method,” Journal of Computational and Applied Mathematics, 2015.
- Dina Tavares, Ricardo Almeida, and Delfim F. M. Torres, “Caputo derivatives of fractional variable order: Numerical approximations,” Communications In Nonlinear Science And Numerical Simulation, vol. 35, pp. 69–87, 2016.
- Michael A. Zhuravkov, and Natalie S. Romanova, “Review of methods and approaches for mechanical problem solutions based on fractional calculus,” Mathematics And Mechanics Of Solids, vol. 21, no. 5, pp. 595–620, 2016.
- Rami Ahmad El-Nabulsi, “Fractional variational approach with non-standard power-law degenerate Lagrangians and a generalized derivative operator,” Tbilisi Mathematical Journal, vol. 9, no. 1, 2016.