Results 11 to 20 of about 370 (174)
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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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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Approximation Algorithm for a System of Pantograph Equations [PDF]
Journal of Applied Mathematics, 2012 We show how to adapt an efficient numerical algorithm to obtain an approximate solution of a system of pantograph equations. This algorithm is based on a combination of Laplace transform and Adomian decomposition method. Numerical examples reveal that the method is quite accurate and efficient, it approximates the solution to a very high degree of ...
Sabir Widatalla, Mohammed Abdulai Koroma
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On the asymptotics of the trapezoidal rule for the pantograph equation [PDF]
Mathematics of Computation, 2009 The paper deals with the trapezoidal rule discretization of a class of linear delay differential equations, with a special emphasis on equations with a proportional delay. Our purpose is to analyse the asymptotic properties of the numerical solutions and formulate their upper bounds.
Jan Cermák, Jirí Jánský
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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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The stability analysis of a discretized pantograph equation [PDF]
Mathematica Bohemica, 2011 Summary: The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index.
Jánský, J., Kundrát, Petr
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Runge–Kutta methods for the multi-pantograph delay equation [PDF]
Applied Mathematics and Computation, 2005 The multi-pantograph equation is a delay differential equation of the form \(u'(t) = \lambda u(t) + \mu_1 u(q_1 t) + \mu_2 u(q_2 t) + \cdots + \mu_l u(q_l t)\), with given initial value \(u(0)\).
D. Li, M. Z. Liu
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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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Stability analysis of pantograph under frictional force
Nihon Kikai Gakkai ronbunshu, 2019 The frictional force acts to the travelling pantograph head in horizontal direction due to sliding of the pantograph head and contact wire. Therefore, vertical motion of the pantograph head is generated by link mechanism of the pantograph.
Shigeyuki KOBAYASHI +2 more
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Energies, 2020 The pantograph catenary system plays an important role in the power performance of electric mining vehicles. A pantograph catenary system combining both a pantograph and a catenary is one of the most promising solutions.
Yinping Li, Tianxu Jin, Li Liu, Kun Yuan
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