Constrained fractional variational problems of variable order
نویسندگان
چکیده
منابع مشابه
Variational formulation of problems involving fractional order differential operators
In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to non-symmetric boundary value problems, which are investigated from a variational point of view. The variational problem for the Riemann-Liouville case is coercive on the space H α/2 0 (0, 1) but the ...
متن کاملManifold Constrained Variational Problems
The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained to remain on a C m-dimensional manifold M ⊂ R is obtained. If f : Rd×N → [0,∞) is a continuous function satisfying 0 ≤ f(ξ) ≤ C(1 + |ξ|), for C > 0, p ≥ 1, and for all ξ ∈ Rd×N , then F(u,Ω) : = inf {un} lim inf n→∞ Z Ω f(∇un) dx : un ⇀ u in W , un(x) ∈M a.e. x ∈ Ω, n ∈ ...
متن کاملFractional Action-like Variational Problems *
Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations. 2000 Mathematics Subject Classification: 49K10, 49S05.
متن کاملDiscrete-time fractional variational problems
We introduce a discrete-time fractional calculus of variations on the time scale hZ, h > 0. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of ...
متن کاملHigher Order Variational Problems
Higher order variational problems appear often in the engineering literature and in connection with the so-called gradient theories of phase transitions within elasto-plastic regimes. The study of equilibria of micromagnetic materials asks for mastery of second order energies (see [51], [91]; see also [31], [38], [44], [45], [61], [77], [78], [79], [108]), and the Blake-Zisserman model for imag...
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: IEEE/CAA Journal of Automatica Sinica
سال: 2017
ISSN: 2329-9266,2329-9274
DOI: 10.1109/jas.2017.7510331