Generalized Fractional Calculus of Variations

Autor:	Odzijewicz, Tatiana
Rok vydání:	2014
Předmět:	Mathematics - Optimization and Control 26A33 49K05 49K21
Druh dokumentu:	Working Paper
Popis:	In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In particular, we obtain necessary optimality conditions of Euler-Lagrange type for the fundamental and isoperimetric problems, natural boundary conditions, and Noether theorems. Existence of solutions is shown under Tonelli type conditions. Moreover, we apply our results to prove existence of eigenvalues, and corresponding orthogonal eigenfunctions, to fractional Sturm-Liouville problems. Comment: PhD thesis, Doctoral Programme in Mathematics and Applications (PDMA), University of Aveiro and University of Minho, 2013. Supervisor: Delfim F. M. Torres; co-supervisor: Agnieszka B. Malinowska. Defended and approved 18-Sept-2013. See http://hdl.handle.net/10773/11731. University of Aveiro, PhD thesis, 2013
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1403.4379 Zobrazit plný text záznamu View this record from Arxiv