Results 51 to 60 of about 2,154 (104)

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  

Stability analysis of discrete‐time systems with a time‐varying delay via improved methods

IET Control Theory &Applications, Volume 18, Issue 7, Page 951-959, April 2024.
This paper studiesthe stability problem for discrete‐time systems with a time‐varying delay by developing a new combined summation inequality and improving a transformation lemma. Numerical examples show that, compared to several recently reported results, the obtained stability condition not only produces larger maximal allowable upper bounds but also
Hongjia Sha, Ju H. Park, Jun Chen, Mingbo Zhu, Chengjie Nan   +4 more
wiley   +1 more source

Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula

Journal of Inequalities and Applications
In 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, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık   +3 more
doaj   +1 more source

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

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

A unified approach to higher order discrete and smooth isoperimetric inequalities

Mathematika, Volume 70, Issue 1, January 2024.
Abstract We present a unified approach to derive sharp isoperimetric‐type inequalities of arbitrary high order. In particular, we obtain (i) sharp high‐order discrete polygonal isoperimetric‐type inequalities, (ii) sharp high‐order isoperimetric‐type inequalities for smooth curves with both upper and lower bounds for the isoperimetric deficit, and (iii)
Kwok‐Kun Kwong
wiley   +1 more source

Switched Observer‐Based Event‐Triggered Safety Control for Delayed Networked Control Systems Under Aperiodic Cyber attacks

International Journal of Intelligent Systems, Volume 2024, Issue 1, 2024.
The networked control systems (NCSs) under cyberattacks have received much attention in both industrial and academic fields, with rare attention on the delayed networked control systems (DNCSs). In order to well address the control problem of DNCSs, in this study, we consider the resilient event‐triggered safety control problem of the NCSs with time ...
Shuqi Li, Yiren Chen, Wenli Shang, Feiqi Deng, Xiaobin Gao, Yu-An Tan   +5 more
wiley   +1 more source

Wirtinger-Type Inequalities Involving Tempered Ψ-Fractional Derivatives with Applications

Fractal and Fractional
In this work, we explore Wirtinger-type inequalities involving tempered Ψ-Caputo fractional derivatives by utilizing Taylor’s formula. We establish more general inequalities for the same operator in Lp norms for p>1 by using Hölder’s inequality.
Qingzhe Wu, Muming Zhang, Jing Shao, Muhammad Samraiz, Humaira Javaid, Saima Naheed   +5 more
doaj   +1 more source

Event-Based Fuzzy H_∞ Control for Unreliable Nonlinear Networked Systems

IEEE Access
The nonlinear Networked Control Systems (NCSs) analyzed in this study not only has packet loss, but also has induced-delay. For this kind of complex systems, this manuscript presents an effective scheme for addressing the Interval Type-2 (IT2) $H_ ...
Zifang Qu, Zhenbin Du, Guangyong Zhang, Xiaohong Sun   +3 more
doaj   +1 more source

Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part

Journal of Inequalities and Applications, 2006
We study nonlinear ODE problems in the complex Euclidean space, with the right-hand side being polynomial with nonconstant periodic coefficients. As the coefficients functions, we admit only functions with vanishing Fourier coefficients for negative ...
Marzantowicz Wacław, Borisovich Andrei   +1 more
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