Title :
Variable order fractional variational calculus for double integrals
Author :
Odzijewicz, T. ; Malinowska, Agnieszka B. ; Torres, Delfim F. M.
Author_Institution :
Dept. of Math., Univ. of Aveiro, Aveiro, Portugal
Abstract :
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green´s theorem are proved. These results allow us to obtain a fractional Euler-Lagrange necessary optimality condition for variable order two-dimensional fractional variational problems.
Keywords :
integration; variational techniques; Green´s theorem; double integrals; fractional Euler-Lagrange necessary optimality condition; partial fractional integrals; partial fractional operators; variable order fractional variational calculus; variable order two-dimensional fractional variational problems; Educational institutions; Equations; Fractional calculus; Integral equations; Optimal control; Green´s theorem; Variable order fractional calculus; fractional calculus of variations; optimality conditions;
Conference_Titel :
Decision and Control (CDC), 2012 IEEE 51st Annual Conference on
Conference_Location :
Maui, HI
Print_ISBN :
978-1-4673-2065-8
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2012.6426489
