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Optimal control problem and maximum principle for fractional order cooperative systems

G. M. Bahaa (2019)

Kybernetika

In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered optimal...

Optimal estimates for the fractional Hardy operator

Yoshihiro Mizuta, Aleš Nekvinda, Tetsu Shimomura (2015)

Studia Mathematica

Let $A_{α} f (x) = {| B (0, | x |) |}^{- α / n} \int_{B (0, | x |)} f (t) d t$ be the n-dimensional fractional Hardy operator, where 0 < α ≤ n. It is well-known that $A_{α}$ is bounded from $L^{p}$ to $L^{p_{α}}$ with $p_{α} = n p / (α p - n p + n)$ when n(1-1/p) < α ≤ n. We improve this result within the framework of Banach function spaces, for instance, weighted Lebesgue spaces and Lorentz spaces. We in fact find a ’source’ space $S_{α, Y}$ , which is strictly larger than X, and a ’target’ space $T_{Y}$ , which is strictly smaller than Y, under the assumption that $A_{α}$ is bounded from X into Y and the Hardy-Littlewood maximal operator...

Ordinary differential equations the solution of which are $A C G_{*}$ -functions

Jaroslav Kurzweil, Štefan Schwabik (1990)

Archivum Mathematicum

O-Regualarly Varying Functions

S. Aljančić, D. Aranđelović (1977)

Publications de l'Institut Mathématique

O-Regular Variation And Uniform Convergence

D. Aranđelović (1990)

Publications de l'Institut Mathématique

Orlicz spaces, α-decreasing functions, and the Δ₂ condition

Gary M. Lieberman (2004)

Colloquium Mathematicae

We prove some quantitatively sharp estimates concerning the Δ₂ and ∇₂ conditions for functions which generalize known ones. The sharp forms arise in the connection between Orlicz space theory and the theory of elliptic partial differential equations.

Orlicz-Morrey spaces and the Hardy-Littlewood maximal function

Eiichi Nakai (2008)

Studia Mathematica

We prove basic properties of Orlicz-Morrey spaces and give a necessary and sufficient condition for boundedness of the Hardy-Littlewood maximal operator M from one Orlicz-Morrey space to another. For example, if f ∈ L(log L)(ℝⁿ), then Mf is in a (generalized) Morrey space (Example 5.1). As an application of boundedness of M, we prove the boundedness of generalized fractional integral operators, improving earlier results of the author.

Orthogonal Polynomials and Regularly Varying Sequences

Slavko Simić (2001)

Publications de l'Institut Mathématique

Orthogonally additive functionals on $B V$

Khaing Aye Khaing, Peng Yee Lee (2004)

Mathematica Bohemica

In this paper we give a representation theorem for the orthogonally additive functionals on the space $B V$ in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.

Oscillating multipliers on noncompact symmetric spaces.

Saverio Giulini, Stefano Meda (1990)

Journal für die reine und angewandte Mathematik

Ostrowski, Grüss, Čebyšev type inequalities for functions whose second derivatives belong to $L_{p} (a, b)$ and whose modulus of second derivatives are convex.

Rafiq, Arif, Ahmad, Farooq (2007)

Revista Colombiana de Matemáticas

Outer $γ$ -convex functions on a normed space.

Phan Thanh An (2005)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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