Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions.
Existence Results for Fractional Functional Differential Inclusions with Infinite Delay and Applications to Control Theory
Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05In this paper we investigate the existence of solutions for fractional functional differential inclusions with infinite delay. In the last section we present an application of our main results in control theory.
Existence results for impulsive fractional differential equations with -Laplacian via variational methods
This paper presents several sufficient conditions for the existence of at least one classical solution to impulsive fractional differential equations with a -Laplacian and Dirichlet boundary conditions. Our technical approach is based on variational methods. Some recent results are extended and improved. Moreover, a concrete example of an application is presented.
Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions.
Existence results for systems of conformable fractional differential equations
In this article, we study the existence of solutions to systems of conformable fractional differential equations with periodic boundary value or initial value conditions. where the right member of the system is -carathéodory function. We employ the method of solution-tube and Schauder’s fixed-point theorem.
Existence results of positive solutions to fractional differential equation with integral boundary conditions
In this paper we consider the existence, multiplicity, and nonexistence of positive solutions to fractional differential equation with integral boundary conditions. Our analysis relies on the fixed point index.
Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces.
Expansions of the real line by open sets: o-minimality and open cores
The open core of a structure ℜ := (ℝ,<,...) is defined to be the reduct (in the sense of definability) of ℜ generated by all of its definable open sets. If the open core of ℜ is o-minimal, then the topological closure of any definable set has finitely many connected components. We show that if every definable subset of ℝ is finite or uncountable, or if ℜ defines addition and multiplication and every definable open subset of ℝ has finitely many connected components, then the open core of ℜ is...
Explicit solutions of some fractional partial differential equations via stable subordinators.
Exponential stability for the wave equation with weak nonmonotone damping.
Extended fractional calculus of variations, complexified geodesics and Wong's fractional equations on complex plane and on Lie algebroids
In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler-Lagrange geodesics and Wong's fractional equations are derived. Many interesting consequences are explored.
Extending times differentiable functions of several variables
It is shown that times Peano differentiable functions defined on a closed subset of and satisfying a certain condition on that set can be extended to times Peano differentiable functions defined on if and only if the th order Peano derivatives are Baire class one functions.
Extending n-convex functions
We are given data α₁,..., αₘ and a set of points E = x₁,...,xₘ. We address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions , i = 1,...,m, that is also n-convex on a set properly containing E. We consider both one-point extensions of E, and extensions to all of ℝ. We also determine bounds on the n-convex functions satisfying the above interpolation conditions.
Extending Peano derivatives
Let be a closed set, a positive integer and a function defined on so that the -th Peano derivative relative to exists. The major result of this paper is that if has finite Denjoy index, then has an extension, , to which is times Peano differentiable on with on for .
Extending Peano derivatives: necessary and sufficient conditions
The paper treats functions which are defined on closed subsets of [0,1] and which are k times Peano differentiable. A necessary and sufficient condition is given for the existence of a k times Peano differentiable extension of such a function to [0,1]. Several applications of the result are presented. In particular, functions defined on symmetric perfect sets are studied.
Extension of differentiable functions
Extension of functions with small oscillation
A classical theorem of Kuratowski says that every Baire one function on a subspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer gradation of Baire one functions into small Baire classes. A Baire one function f is assigned into a class in this hierarchy depending on its oscillation index β(f). We prove a refinement of Kuratowski’s theorem: if Y is a subspace of a metric space X and f is a real-valued...
Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps
We prove an abstract version of the Kuratowski extension theorem for Borel measurable maps of a given class. It enables us to deduce and improve its nonseparable version due to Hansell. We also study the ranges of not necessarily injective Borel bimeasurable maps f and show that some control on the relative classes of preimages and images of Borel sets under f enables one to get a bound on the absolute class of the range of f. This seems to be of some interest even within separable spaces.
Extrait d'une Lettre adressée à M. Besge.
Extrait d'une lettre adressée à M. Hermite