A fractional calculus of variations for multiple integrals with application to vibrating string

被引：111

作者：

Almeida, Ricardo ^{[1
]}

Malinowska, Agnieszka B. ^{[1
,2
]}

Torres, Delfim F. M. ^{[1
]}

机构：

[1] Univ Aveiro, Dept Math, P-3810193 Aveiro, Portugal

[2] Bialystok Tech Univ, Fac Comp Sci, PL-15351 Bialystok, Poland

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2010年 / 51卷 / 03期

关键词：

calculus; Green's function methods; integral equations; NONDIFFERENTIABLE FUNCTIONS; LAGRANGIAN MECHANICS; BROWNIAN-MOTION; DERIVATIVES; HAMILTON; FORMALISM; SYSTEMS; THEOREM; SERIES; ORDER;

D O I：

10.1063/1.3319559

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. The main results provide fractional versions of the theorems of Green and Gauss, fractional Euler-Lagrange equations, and fractional natural boundary conditions. As an application we discuss the fractional equation of motion of a vibrating string.

引用

页数：12

共 43 条

[1] Fractional variational calculus and the transversality conditions [J].