Results 61 to 70 of about 2,976 (212)

Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations

Complexity, 2022
A new class of polynomials investigates the numerical solution of the fractional pantograph delay ordinary differential equations. These polynomials are equipped with an auxiliary unknown parameter a, which is obtained using the collocation and least ...
Jalal Hajishafieiha, Saeid Abbasbandy
doaj   +1 more source

On the advanced balanced pantograph equation

Communications on Pure and Applied Analysis
The paper is concerned with the advanced balanced pantograph equation \[ y'(x)+y(x)=\displaystyle\sum_{k=1}^m p_k y(a_kx),\tag{1} \] where \(p_k>0\) for \(k=1,\ldots,m\), \(\sum_{k=1}^m p_k=1\), and ...
van Brunt, Bruce, Derfel, Gregory, Zaidi, Ali Ashher   +2 more
openaire   +2 more sources

Active Power Filter‐Based Low‐Frequency Ripple Power Suppression of the DC‐Link in Railway Traction Systems

IET Power Electronics, Volume 19, Issue 1, January/December 2026.
This article presents an active power filtering control method to suppress ripple power in the DC‐link of railway traction systems, including both the inherent second‐order ripple of single‐phase rectifiers and additional frequency ripples introduced by the pantograph–catenary arc.
Wei Wang, Wei Jiang, Hao Yue, Xiangmin He, Xinke Wang, Wensheng Song   +5 more
wiley   +1 more source

Bionic Optimization and Aerodynamic Performance Analysis of High-speed Train Pantograph

Journal of Applied Science and Engineering
The aerodynamic drag of a high-speed train has a significant impact on its energy consumption. At high speeds, the pantograph is one of the primary sources of aerodynamic drag for the train.
Qi Zhou, Zhenfeng Wu, Longhui Zhu
doaj   +1 more source

Exact and Approximate Solutions for Some Classes of the Inhomogeneous Pantograph Equation

Axioms, 2023
The standard pantograph delay equation (SPDDE) is one of the famous delay models. This standard model is basically homogeneous in nature and it has been extensively studied in the literature. However, the studies on the general inhomogeneous form of such
A. A. Al Qarni
doaj   +1 more source

Energy efficiency and integration of urban electrical transport systems: EVS and metro-trains of two real European lines [PDF]

, 2019
Transport is a main source of pollutants in cities, where air quality is a major concern. New transport technologies, such as electric vehicles, and public transport modalities, such as urban railways, have arisen as solutions to this important problem ...
Cucala, Asunción P., Falvo, Maria Carmen, Fernández-Cardador, Antonio, Fernández-Rodríguez, Adrián   +3 more
core   +1 more source

On Bounded Solutions of the Balanced Generalized Pantograph Equation [PDF]

, 2008
The question about the existence and characterization of bounded solutions to linear functional-differential equations with both advanced and delayed arguments was posed in early 1970s by T. Kato in connection with the analysis of the pantograph equation, y'(x)=ay(qx)+by(x).
Bogachev, Leonid, Derfel, Gregory, Molchanov, Stanislav, Ockendon, John   +3 more
openaire   +2 more sources

Fractional Integral Inequalities for Generalized Interval‐Valued Functions With Applications in Stock Price Prediction via LSTM

Journal of Mathematics, Volume 2026, Issue 1, 2026.
We explore the features of fractional integral inequalities for some new classes of interval‐valued convex functions (CF s) to establish their generalization compared to the previously known real‐valued CF s. Motivated by the foundational role of mathematical inequalities in analysis and optimization, we delve into the formulation and proof of integral
Ahsan Fareed Shah, Patricia J. Y. Wong, Nasir Rehman, Salah Mahmoud Boulaaras, Muhammad Shoaib Saleem, B. B Upadhyay   +5 more
wiley   +1 more source

Dynamical analysis of Hilfer–Hadamard type fractional pantograph equations via successive approximation

Journal of Taibah University for Science, 2019
In this note, we consider a nonlinear pantograph equation with Hilfer–Hadamard fractional derivative. We investigate the existence and continuous dependence results by using successive approximations and generalized Gronwall inequality.
D. Vivek, Kamal Shah, K. Kanagarajan
doaj   +1 more source

Nonfragile Sliding Mode Control of Fractional‐Order Complex Networked Systems via Combination Event‐Triggered Approach

International Journal of Robust and Nonlinear Control, Volume 35, Issue 13, Page 5685-5704, 10 September 2025.
ABSTRACT This work addresses the problem of developing a nonfragile sliding mode observer for fractional‐order complex networked systems (FO‐CNS) under stochastic network attacks. The proposed approach employs a combination of event‐triggered techniques. First, a nonfragile fractional‐order state observer is developed, enabling the design of a suitable
Xin Meng, Baoping Jiang, Hamid Reza Karimi   +2 more
wiley   +1 more source