Results 21 to 30 of about 600,406 (168)
A more generalized Gronwall-like integral inequality with applications
International Journal of Mathematics and Mathematical Sciences, 2003 This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992).
Qinghua Ma, Lokenath Debnath
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A Gronwall inequality for a general Caputo fractional operator [PDF]
, 2017 In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo--Hadamard fractional derivative operators.
R. Almeida
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From the Newton equation to the wave equation : the case of shock waves [PDF]
, 2016 We study the macroscopic limit of a chain of atoms governed by the Newton equation. It is known from the work of Blanc, Le Bris, Lions, that this limit is the solution of a nonlinear wave equation, as long as this solution remains smooth.
Blanc, Xavier, Josien, Marc
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A Gronwall inequality via the generalized proportional fractional derivative with applications
Journal of Inequalities and Applications, 2019 In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its ...
J. Alzabut +3 more
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On Some Vector-Valued Inequalities of Gronwall Type
Abstract and Applied Analysis, 2014 In this paper we established some vector-valued inequalities of Gronwall type in ordered Banach spaces. Our results can be applied to investigate systems of real-valued Gronwall-type inequalities.
Dah-Chin Luor
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Ulam stability and data dependence for fractional differential equations with Caputo derivative
Electronic Journal of Qualitative Theory of Differential Equations, 2011 In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order $\alpha$ are studied. We present four types of Ulam stability results for the fractional differential equation in the case ...
JinRong Wang, Linli Lv, Yong Zhou
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A Generalized Gronwall Inequality for Caputo Fractional Dynamic Delta Operator [PDF]
Progress in Fractional Differentiation and Applications, 2019 In this paper we obtain generalized Gronwall type inequality using Caputo Fractional delta operator. Also we have obtained the existence of solution of Cauchy's Type problem on fractional dynamic equations using dynamic delta operator.
D. Pachpatte
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On the Hyers-Ulam Stability of First-Order Impulsive Delay Differential Equations
Journal of Function Spaces, 2016 This paper proves the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of nonlinear first-order ordinary differential equation with single constant delay and finite impulses on a compact interval.
Akbar Zada, Shah Faisal, Yongjin Li
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Finite element convergence analysis for the thermoviscoelastic Joule heating problem [PDF]
, 2017 We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical component that can be used e.g.
Målqvist, Axel, Stillfjord, Tony
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International Journal of Mathematics and Mathematical Sciences, 1991 By using the Gronwall Bellman inequality we prove some limit relations between the solutions of delay differential equations with continuous arguments and the solutions of some related delay differential equations with piecewise constant arguments(EPCA).
Istevan Györi
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