Related papers: Composition Functionals in Fractional Calculus of …
In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo…
In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of…
Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…
We discover a new minimality property of the absolute minimisers of supremal functionals (also known as $L^\infty$ Calculus of Variations problems).
Using the concept of fractional derivatives of Riemann$-$Liouville on time scales, we first introduce right fractional Sobolev spaces and characterize them. Then, we prove the equivalence of some norms in the introduced spaces, and obtain…
Within the geometrical framework developed in arXiv:0705.2362, the problem of minimality for constrained calculus of variations is analysed among the class of differentiable curves. A fully covariant representation of the second variation…
We present an extension of some results of higher order calculus of variations and optimal control to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing…
We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke functional framework and present minimization properties,…
We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped…
This article examines a new approach to solving ordinary differential equations based on Fractional-Calculus theory. Poisson and Sturm-Liouville-type problems are studied, together with different boundary conditions. Each case is analyzed…
The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…
In this work we prove a strong maximum principle for fractional elliptic problems with mixed Dirichlet-Neumann boundary data which extends the one proved by J. D\'avila to the fractional setting. In particular, we present a comparison…
Starting from the Riemann-Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated…
We formulate fractional difference equations of Riemann-Liouville and Caputo type in a functional analytical framework. Main results are existence of solutions on Hilbert space-valued weighted sequence spaces and a condition for stability…
In this paper we study a variational Neumann problem for the higher order $s$-fractional Laplacian, with $s>1$. In the process, we introduce some non-local Neumann boundary conditions that appear in a natural way from a Gauss-like…
We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cannot be solved using the classical theory.
We extend the notion of variational integrator for classical Euler-Lagrange equations to the fractional ones. As in the classical case, we prove that the variational integrator allows to preserve Noether-type results at the discrete level.
The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.
A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented. This includes Dirichlet, mixed, Robin, fractional, Sturm-Liouville, integral, nonlocal,…
The theory of perfect fluids is reconsidered from the point of view of a covariant Lagrangian theory. It has been shown that the Euler-Lagrange equations for a perfect fluid could be found in spaces with affine connections and metrics from…