FRACTIONAL CALCULUS OF VARIATIONS FOR A COMBINED CAPUTO DERIVATIVE

被引：60

作者：

Malinowska, Agnieszka B. ^{[1
]}

Torres, Delfim F. M. ^{[2
]}

机构：

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

[2] Univ Aveiro, Dept Math, Ctr Res & Dev Math, P-3810193 Aveiro, Portugal

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2011年 / 14卷 / 04期

关键词：

fractional derivatives; Caputo derivatives; fractional variational principles; Euler-Lagrange equations; isoperimetric constraints; transversality conditions; NATURAL BOUNDARY-CONDITIONS; EULER-LAGRANGE EQUATIONS; HAMILTON FORMALISM; CONSERVATION-LAWS; FORMULATION; TERMS; MECHANICS; INTEGRALS; ALPHA;

D O I：

10.2478/s13540-011-0032-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We generalize the fractional Caputo derivative to the fractional derivative (C)D(gamma)(alpha,beta), which is a convex combination of the left Caputo fractional derivative of order a and the right Caputo fractional derivative of order beta. The fractional variational problems under our consideration are formulated in terms of (C)D(gamma)(alpha,beta). The Euler-Lagrange equations for the basic and isoperimetric problems, as well as transversality conditions, are proved.

引用

页码：523 / 537

页数：15

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