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Continuity and Differentiability of Solutions with Respect to Initial Conditions and Peano Theorem for Uncertain Differential Equations
- Source :
- Mathematics Interdisciplinary Research, Vol 7, Iss 3, Pp 249-260 (2022)
- Publication Year :
- 2022
- Publisher :
- University of Kashan, 2022.
-
Abstract
- In this paper we study the dependence of solutions of uncertain initial value problems (UIVP) on the initial values. Introducing a contraction mapping and using Banach Fixed Point Theorem (BFPT), the existence and uniqueness (EaU) of solutions of the UIVP will be proven. We show that under appropriate assumptions, the solutions of UIVP are continues and differentiable with respect to initial conditions (ICs). The paper will be ended by proving a theorem about the existence of solutions of an autonomous UIVP under weaker conditions. This theorem is a generalization of PeanoTheorem to UDEs.
Details
- Language :
- English
- ISSN :
- 24764965
- Volume :
- 7
- Issue :
- 3
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematics Interdisciplinary Research
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.6e462c28cedb49728880800a7f3d3c59
- Document Type :
- article
- Full Text :
- https://doi.org/10.22052/mir.2022.246010.1337