Results 21 to 30 of about 588 (178)
Best possible gronwall inequalities
Mathematical and Computer Modelling, 1997 The authors have obtained upper estimates on the inequalities of the form \[ u_{n+ 1}\leq T_n\{u\},\quad n= 1,2,\dots, \] by using the monotonicity of the operators involved. The mathematical induction is used to establish the results in the paper.
Magnucka-Blandzi, E. +2 more
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A Gronwall-type Trigonometric Inequality [PDF]
The American Mathematical Monthly, 2018 We prove that the absolute value of the $n$th derivative of $\cos(\sqrt{x})$ does not exceed $n!/(2n)!$ for all $x>0$ and $n = 0,1,\ldots$ and obtain a natural generalization of this inequality involving the analytic continuation of $\cos(\sqrt{x})$.
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On the Hyers-Ulam Stability of Differential Equations of Second Order
Abstract and Applied Analysis, 2014 By using of the Gronwall inequality, we prove the Hyers-Ulam stability of differential equations of second order with initial conditions.
Qusuay H. Alqifiary, Soon-Mo Jung
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Robust finite-time stability of neutral fractional time-delay systems
上海师范大学学报. 自然科学版, 2020 This paper is devoted to investigating the robust finite-time stability issue of neutral fractionalorder system. Based on the generalized Bellman-Gronwall inequality, a new sufficient condition is established for the particular class of neutral ...
ZHANG Li, GAO Cunchen, REN Qifeng
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A new approach to interval-valued inequalities
Advances in Difference Equations, 2020 The objective of this work is to advance and simplify the notion of Gronwall’s inequality. By using an efficient partial order and concept of gH-differentiability on interval-valued functions, we investigate some new variants of Gronwall type ...
Awais Younus +4 more
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Concept and application of interval-valued fractional conformable calculus
Alexandria Engineering Journal, 2022 This paper introduces a new concept of Caputo type interval-valued fractional conformable calculus. Based on this, some theorems and properties related to fractional conformable calculus are presented.
Lihong Zhang +3 more
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Generalizations of Gronwall–Bihari inequalities on time scales [PDF]
Journal of Difference Equations and Applications, 2009 This is a preprint of an article accepted (16/May/2008) for publication in the "Journal of Difference Equations and Applications"; J. Difference Equ. Appl.
Ferreira, R.A.C., Torres, D.F.M.
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Journal of Function Spaces, 2021 A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson method, and ...
Lili Li, Mianfu She, Yuanling Niu
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New finite-time stability result for a class of Itô-Doob stochastic fractional order systems
Alexandria Engineering Journal, 2023 In this article, we study the Finite-Time Stability (FTS) of Linear Stochastic Fractional Differential Equations of Itô-Doob Type with Delay (LSFDEIDTwD) for a derivative order ρ∈(0,1).
Hassen Arfaoui +3 more
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Gronwall's Inequality in n Independent Variables [PDF]
Proceedings of the American Mathematical Society, 1973 The paper presents an extension of Gronwall's inequality to n independent variables. The inequality is established by solving a characteristic initial value problem by the Riemann method. Thus a Riemann function associated with a hyperbolic partial differential equation appears in the inequality.
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