University of KashanMathematics Interdisciplinary Research2538-36397320220901Continuity and Differentiability of Solutions with Respect to Initial Conditions and Peano Theorem for Uncertain Differential Equations24926011208210.22052/mir.2022.246010.1337ENVahidRoomiDepartment of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. Iran0000000221556433Hamid RezaAhmadiDepartment of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. IranJournal Article20220207 <span class="fontstyle0">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 Peano<br />Theorem to UDEs.</span>https://mir.kashanu.ac.ir/article_112082_9aeedad657247890a3f51c9aa5996e09.pdf