Results 41 to 50 of about 353 (183)
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
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On Stability of Second Order Pantograph Fractional Differential Equations in Weighted Banach Space
Fractal and Fractional, 2023 This work investigates a weighted Banach space second order pantograph fractional differential equation. The considered equation is of second order, expressed in terms of the Caputo–Hadamard fractional operator, and constructed in a general manner to ...
Ridha Dida +5 more
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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 +5 more
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MathematicsThis paper solves a nonhomogeneous version of the pantograph equation. The nonhomogeneous term is taken as a polynomial of degree n with arbitrary coefficients.
Mona D. Aljoufi
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AIMS MathematicsIn this research, we investigated the Riemann-Liouville fractional-order pantograph differential equation constrained by nonlocal and weighted pantograph integral constraints. We presented novel sufficient conditions for the uniqueness of the solution.
Ahmed M. A. El-Sayed +3 more
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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 +2 more
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On the advanced balanced pantograph equation
Communications on Pure and Applied AnalysisThe 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 +2 more
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Engineering Reports, Volume 7, Issue 8, August 2025.Railway electrification systems indeed have unique challenges due to variable power demand and dynamic train operations. Power quality (PQ) monitoring for high‐speed trains (HSTs) is essential to guarantee the effectual and unfailing operation of the ESs.
Pampa Sinha +6 more
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Bionic Optimization and Aerodynamic Performance Analysis of High-speed Train Pantograph
Journal of Applied Science and EngineeringThe 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
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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 +3 more
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