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Hamilton’s Principle with Variable Order Fractional Derivatives

Atanackovic, Teodor, Pilipovic, Stevan (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler–Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive equation....

Hardy and Rellich type inequalities with remainders

Ramil Nasibullin (2022)

Czechoslovak Mathematical Journal

Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean space. We obtain one-dimensional Hardy type inequalities and their multidimensional analogues in convex domains with the finite inradius. We use Bessel functions and the Lamb constant. The statements proved are a generalization for the case of arbitrary $p\geq 2$ of the corresponding inequality proved by F. G. Avkhadiev, K.-J. Wirths (2011) for $p = 2$....

Hardy Inequality in Variable Exponent Lebesgue Spaces

Diening, Lars, Samko, Stefan (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26D10, 46E30, 47B38We prove the Hardy inequality and a similar inequality for the dual Hardy operator for variable exponent Lebesgue spaces.

Hardy-Poincaré type inequalities derived from p-harmonic problems

Iwona Skrzypczak (2014)

Banach Center Publications

We apply general Hardy type inequalities, recently obtained by the author. As a consequence we obtain a family of Hardy-Poincaré inequalities with certain constants, contributing to the question about precise constants in such inequalities posed in [3]. We confirm optimality of some constants obtained in [3] and [8]. Furthermore, we give constants for generalized inequalities with the proof of their optimality.

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