Results 81 to 90 of about 2,994 (165)
An extension of the complex–real (C–R) calculus to the bicomplex setting, with applications
Mathematische Nachrichten, Volume 297, Issue 2, Page 454-481, February 2024.Abstract In this paper, we extend notions of complex C−R$\mathbb {C} - \mathbb {R}$‐calculus to the bicomplex setting and compare the bicomplex polyanalytic function theory to the classical complex case. Applications of this theory include two bicomplex least mean square algorithms, which extend classical real and complex least mean square algorithms.
Daniel Alpay, Kamal Diki, Mihaela Vajiac
wiley +1 more source
On Generalized Wirtinger Inequalities for (k,ψ)-Caputo Fractional Derivatives and Applications
Fractal and FractionalThe primary aim of this study is to establish new Wirtinger-type inequalities involving fractional derivatives, which are essential tools in analysis and applied mathematics.
Muhammad Samraiz +2 more
doaj +1 more source
Discrete analogs of inequalities of Wirtinger
Monatshefte f�r Mathematik, 1955 In the theory of inequalities there are often encountered inequalities which are first proved for finite series and then established for infinite series or integrals. We shall discuss here the finite analogs of several integral inequalities which appear to have been established directly.
Todd, John, Fan, Ky, Taussky, Olga
openaire +2 more sources
An optimal lower bound in fractional spectral geometry for planar sets with topological constraints
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We prove a lower bound on the first eigenvalue of the fractional Dirichlet–Laplacian of order s$s$ on planar open sets, in terms of their inradius and topology. The result is optimal, in many respects. In particular, we recover a classical result proved independently by Croke, Osserman, and Taylor, in the limit as s$s$ goes to 1.
Francesca Bianchi, Lorenzo Brasco
wiley +1 more source
On discrete inequalities of Wirtinger's type
Journal of Mathematical Analysis and Applications, 1982 AbstractDiscrete inequalities of Wirtinger's type are considered. Constants in the obtained inequalities are the best ones. In the special case the inequalities (1) and (2) are obtained. They are proved by K. Fan, O. Taussky, and J. Todd: Discrete analogs of inequalities of Wirtinger, Montash. Math. 59 (1955), 73–79.
Milovanović, Gradimir V +1 more
openaire +1 more source
Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula
Journal of Inequalities and ApplicationsIn this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional ...
Samet Erden +3 more
doaj +1 more source
Lyapunov's Type Inequalities for Fourth-Order Differential Equations
Abstract and Applied Analysis, 2012 For a fourth-order differential equation, we will establish some new Lyapunov-type inequalities, which give lower bounds of the distance between zeros of a nontrivial solution and also lower bounds of the distance between zeros of a solution and/or its ...
Samir H. Saker
doaj +1 more source
Picone's identity for a system of first-order nonlinear partial differential equations
Electronic Journal of Differential Equations, 2013 We established a Picone identity for systems of nonlinear partial differential equations of first-order. With the help of this formula, we obtain qualitative results such as an integral inequality of Wirtinger type and the existence of zeros for the ...
Jaroslav Jaros
doaj
IEEE Access, 2018 This paper addresses the stabilization problem of direct current (DC) microgrids through distributed controller design that employs event-based strategy to reduce data communication. The considered dc microgrid is composed of multiple-photovoltaic arrays
Zhixiong Zhong
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Static anti-windup compensator design for locally Lipschitz systems under input and output delays. [PDF]
PLoS One, 2023 Hameed MJ +5 more
europepmc +1 more source