FRACTIONAL h-DIFFERENCE EQUATIONS ARISING FROM THE CALCULUS OF VARIATIONS

被引：139

作者：

Ferreira, Rui A. C. ^{[1
]}

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

机构：

[1] Lusophone Univ Humanities & Technol, Fac Engn & Nat Sci, Dept Math, P-1749024 Lisbon, Portugal

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

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2011年 / 5卷 / 01期

关键词：

Fractional discrete calculus; fractional difference calculus of variations; Euler-Lagrange equations; explicit solutions; DERIVATIVES; SYSTEMS; ENERGY; TERMS;

D O I：

10.2298/AADM110131002F

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The recent theory of fractional h-difference equations introduced in [9], is enriched with useful tools for the explicit solution of discrete equations involving left and right fractional difference operators. New results for the right fractional h sum are proved. Illustrative examples show the effectiveness of the obtained results in solving fractional discrete Euler-Lagrange equations.

引用

页码：110 / 121

页数：12

共 30 条

[1] Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives [J].

Almeida, Ricardo ;

Torres, Delfim F. M. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (03) :1490-1500

[2] Leitmann's direct method for fractional optimization problems [J].

Almeida, Ricardo ;

Torres, Delfim F. M. .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (03) :956-962

[3] Calculus of variations with fractional derivatives and fractional integrals [J].

Almeida, Ricardo ;

Torres, Delfim F. M. .

APPLIED MATHEMATICS LETTERS, 2009, 22 (12) :1816-1820

[4] Nabla discrete fractional calculus and nabla inequalities [J].

Anastassiou, George A. .

MATHEMATICAL AND COMPUTER MODELLING, 2010, 51 (5-6) :562-571

[5]

Atici F M., 2007, International Journal of Difference Equations, V2, P165

[6] Modeling with fractional difference equations [J].

Atici, Ferhan M. ;

Senguel, Sevgi .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 369 (01) :1-9

[7]

Atici FM, 2009, P AM MATH SOC, V137, P981

[8]

Bastos N., 2010, COMMUN FRAC CALC, P41

[9]

Bastos N.R.O., 2011, Int. J. Math. Comput, V11, P1

[10] Discrete-time fractional variational problems [J].

Bastos, Nuno R. O. ;

Ferreira, Rui A. C. ;

Torres, Delfim F. M. .

SIGNAL PROCESSING, 2011, 91 (03) :513-524

← 1 2 3 →