tailieunhanh - báo cáo hóa học:" Research Article Fractional-Order Variational Calculus with Generalized Boundary Conditions"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Fractional-Order Variational Calculus with Generalized Boundary Conditions | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 357580 9 pages doi 2011 357580 Research Article Fractional-Order Variational Calculus with Generalized Boundary Conditions Mohamed A. E. Herzallah1 2 and Dumitru Baleanu3 4 1 Faculty of Science Zagazig University Zagazig Egypt 2 Faculty of Science in Zulfi Majmaah University Zulfi 11932 . Box 1712 Saudi Arabia 3 Department of Mathematics and Computer Science Cankaya University 06530 Ankara Turkey 4 Institute for Space Sciences MG-23 Magurele 76900 Bucharest Romania Correspondence should be addressed to Dumitru Baleanu dumitru@ Received 18 September 2010 Accepted 8 November 2010 Academic Editor J. J. Trujillo Copyright 2011 M. A. E. Herzallah and D. Baleanu. 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. This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points. To illustrate our approach two examples are discussed in detail. 1. Introduction Fractional calculus is one of the generalizations of the classical calculus. Several fields of application of fractional differentiation and fractional integration are already well established some others have just started. Many applications of fractional calculus can be found in turbulence and fluid dynamics stochastic dynamical system plasma physics and controlled thermonuclear fusion nonlinear control theory image processing nonlinear biological systems astrophysics and so forth see 1-11 and the references therein . Real integer variational calculus plays a significant role in many areas of science engineering and applied .