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Sufficient conditions for polynomial asymptotic behaviour of the stochastic pantograph equation [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2016 This paper studies the asymptotic growth and decay properties of solutions of the stochastic pantograph equation with multiplicative noise. We give sufficient conditions on the parameters for solutions to grow at a polynomial rate in $p$-th mean and in ...
John Appleby, Evelyn Buckwar
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Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform
Mathematics, 2023 The Pantograph equation is a fundamental mathematical model in the field of delay differential equations. A special case of the Pantograph equation is well known as the Ambartsumian delay equation which has a particular application in Astrophysics.
Reem Alrebdi, Hind K. Al-Jeaid
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Fractal and Fractional, 2022 The current paper intends to report the existence and uniqueness of positive solutions for nonlinear pantograph Caputo–Hadamard fractional differential equations.
Hamid Boulares +4 more
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An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations
Complexity, 2022 The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ-method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes.
Fathalla A. Rihan, Ahmed F. Rihan
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Axioms, 2023 This paper discusses the problem of the existence and uniqueness of solutions to the boundary value problem for the nonlinear fractional-order pantograph equation, using the fractional derivative of variable order of Hadamard type.
Kadda Maazouz +2 more
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Approximate solutions of hybrid stochastic pantograph equations with Levy jumps [PDF]
, 2013 We investigate a class of stochastic pantograph differential equations with Markovian switching and Levy jumps. We prove that the approximate solutions converge to the true solutions in 퐿 2 sense as well as in probability under local Lipschitz condition ...
Mao, Wei, Mao, Xuerong
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The Energy Benefits of the Pantograph Wing Mechanism in Flapping Flight: Case Study of a Gull [PDF]
, 2015 Bird wings generally contain a 4-bar pantograph mechanism in the forearm that enables the wrist joint to be actuated from the elbow joint thus reducing the number of wing muscles and hence reducing the wing inertia and inertial drag.
Sattler, Gene D.
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Advances in Difference Equations, 2020 This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation.
Idris Ahmed +4 more
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Advances in Mechanical Engineering, 2023 During the operation of high-speed railway, the transition-point disappearance phenomenon, which is caused by the deformation of pantograph head, poses a safety threat to the pantograph-catenary system.
Junqing Chen +5 more
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Assessment of the worthwhileness of efficient driving in railway systems with high-receptivity power supplies [PDF]
, 2020 Eco-driving is one of the most important strategies for significantly reducing the energy consumption of railways with low investments. It consists of designing a way of driving a train to fulfil a target running time, consuming the minimum amount of ...
Cucala, A. P. +4 more
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