Book Reviews
Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces
In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order .
Boundary value problems for differential equations with fractional order.
Boundary value problems for differential inclusions with fractional order
In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
Boundary value problems for Hadamard-Caputo implicit fractional differential inclusions with nonlocal conditions
In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.
Boundary value problems for the Schrödinger equation involving the Henstock-Kurzweil integral
In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation , where and are Henstock-Kurzweil integrable functions on . Results presented in this article are generalizations of the classical results for the Lebesgue integral.
Bounded linear functionals on the space of Henstock-Kurzweil integrable functions
Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence and equality of two iterated Henstock-Kurzweil integrals.
Bounded variation and differentiability of functions.
Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces.
Boundedness properties for functional inequalities.
Boundedness properties of fractional integral operators associated to non-doubling measures
The main purpose of this paper is to investigate the behavior of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed power of its radius. This allows, in particular, non-doubling measures. It turns out that this condition is enough to build up a theory that contains the classical results based upon the Lebesgue measure on Euclidean space and their known extensions for doubling...
Bounds for the 3x+1 problem using difference inequalities
Bounds for the beta function
BV functions with respect to a measure and relaxation of metric integral functionals.
BV-sets, functions and integrals
weakly chaotic functions with zero topological entropy and non- flat critical points.
Calcul d'Ito sans probabilités
Calculation of improper integrals using uniformly distributed sequences
Calculus of Variations with Classical and Fractional Derivatives
MSC 2010: 49K05, 26A33We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.
Canonical Banach function spaces generated by Urysohn universal spaces. Measures as Lipschitz maps
It is proved (independently of the result of Holmes [Fund. Math. 140 (1992)]) that the dual space of the uniform closure of the linear span of the maps x ↦ d(x,a) - d(x,b), where d is the metric of the Urysohn space of diameter r, is (isometrically if r = +∞) isomorphic to the space of equivalence classes of all real-valued Lipschitz maps on . The space of all signed (real-valued) Borel measures on is isometrically embedded in the dual space of and it is shown that the image of the embedding...