Discrete direct methods in the fractional calculus of variations
نویسندگان
چکیده
منابع مشابه
Discrete direct methods in the fractional calculus of variations
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann–Liouville fractional ...
متن کاملDirect methods in the calculus of variations for differential forms
*Correspondence: [email protected] Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China Abstract The purpose of this paper is to establish the general theory of the direct methods to functionals I defined on the Grassmann algebra employing the classical approaches. In this paper, various notions of convexity conditions for weak lower semicontinuity of I are di...
متن کاملFractional calculus of variations for double integrals
We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann–Liouville approach. A necessary optimality condition of Euler–Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. M.S.C. 2010: 49K21, 35R11.
متن کاملCalculus of variations with fractional derivatives and fractional integrals
We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2013
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2013.01.045