Results 91 to 100 of about 485,864 (198)
An Asymptotic Behavior Property of High-Order Nonlinear Dynamic Equations on Time Scales
AxiomsIn this work, by using one dynamic Gronwall–Bihari-type integral inequality on time scales, an interesting asymptotic behavior property of high-order nonlinear dynamic equations on time scales was obtained, which also generalized two classical results ...
Yuan Yuan, Qinghua Ma
doaj +1 more source
Boundedness of the Solutions to Certain Delay Dynamic Integrodifferential Systems on Time Scales
Discrete Dynamics in Nature and Society, 2018 In this paper, the bounds on the solutions of certain delay dynamic integrodifferential systems on time scales are considered. Based on a new Gronwall-Bellman type delay integral inequality, we can estimate the boundedness of solutions to ...
Min Fan, Yazhou Tian
doaj +1 more source
We prove the following version generalization of the Gronwall inequality: Let $\mathbf X$ be a Banach space and $U\subset \mathbf X$ an open convex set in $\mathbf X$. Let $f,g\colon [a,b]\times U\to \mathbf X$ be continuous functions and let $y,z\colon [a,b]\to U$ satisfy the initial value problems \begin{align*} y'(t)&=f(t,y(t)),\quad y(a)=y_0,\\
openaire +2 more sources
The 𝑒-positive mild solutions for fractional impulsive evolution equations with 1 < 𝛼 < 2
CQD Revista Eletrônica Paulista de Matemática, 2022 In this paper, we investigate the existence of global 𝑒-positive mild solutions for impulsive evolution fractional differential equation in the Caputo sense of order 1 < 𝛼 < 2.
Jorge Féres Junior +2 more
doaj
, 2021 Eşitsizlikler, matematiğin birçok dalının gelişmesine katkı sağlar ve çeşitli denklem sınıflarının incelenmesi için gerekli araçlardır. Eşitsizlikler sadece matematikte değil, fen bilimleri ve mühendislik gibi çok çeşitli alanlarda kullanılmaktadır ...
Aruğaslan Çinçin, Duygu, 1979- thesis advisor 71751 +2 more
core
Boundary Value Problems, 2009 By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of ...
Nieto JJ, Stamov GTr, Alzabut JO
doaj
A Gronwall inequality for a general Caputo fractional operator
, 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.
Almeida, Ricardo, Ricardo Almeida
core +1 more source
Some basic theorems on difference-differential equations
Electronic Journal of Differential Equations, 2008 In this paper some basic theorems on the existence, uniqueness and continuous dependence of solutions of a certain difference-differential equation are established.
Baburao G. Pachpatte
doaj
A Nonlinear Generalizations of Dynamic Inequalities on Time Scales
Ratio MathematicaConsidering the distinctive generalization of the Gronwall-Bellman inequality, in this paper we innovates new dynamical inequalities on time scale. These inequalities will be acted a profound tools for studying qualitative properties such as uniqueness ...
Vikas Sopan Jadhav +3 more
doaj +1 more source
Impulsive Problems for Fractional Differential Equations with Nonlocal Boundary Value Conditions
Abstract and Applied Analysis, 2014 We investigate the nonlocal boundary value problems of impulsive fractional differential equations. By Banach’s contraction mapping principle, Schaefer’s fixed point theorem, and the nonlinear alternative of Leray-Schauder type, some related new ...
Peiluan Li, Youlin Shang
doaj +1 more source