WebMar 9, 2024 · The new forms of Gronwall's inequality are obtained within a general platform that includes several existing results as particular cases. To apply our results and examine their validity, we prove the existence and uniqueness of solutions for $ \psi $-fractional initial value problem. Further, the Ulam-Hyers stability of solutions for $ \psi ...

Gronwall Inequality - an overview ScienceDirect Topics

WebDec 1, 1973 · Although the integral inequalities of Gronwall- Bellman type are widely known and used, there appear to be no results of this kind for integral inequalities. 2. The celebrated Gronwall-Bellman lemma and its variants play a vital role in the study of the stability and boundedness properties of differential and integral equations. WebGronwall’s type integral inequality and their discrete analogues have been obtained and used extensively, see for instance [1, 6–9]. In [1], the following generalization of … powerball 10/05/22

Some delay Gronwall type inequalities on time scales

WebNov 3, 2015 · In this paper, we investigate some delay Gronwall type inequalities on time scales by using Gronwall’s inequality. Our results unify and extend some delay integral inequalities and their corresponding discrete analogues. The inequalities given here can be used as handy tools in the qualitative theory of certain classes of delay dynamic … WebIn this video, I state and prove Grönwall’s inequality, which is used for example to show that (under certain assumptions), ODEs have a unique solution. Basi... WebJun 29, 2024 · Among the more recent investigations on interval-valued Gronwall type inequalities, let us mention the work of Younus et al. [39, 40], where the authors obtain Gronwall inequalities for the interval-valued functions under the notion of Kulish–Mirankor partial order on a set of compact intervals. However, there are many other partial orders ... tower records creator