Continuity and Differentiability of Solutions with Respect to Initial Conditions and Peano Theorem for Uncertain Differential Equations

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.

Keywords

• continuity
• differentiability
• uncertain differential equations
• initial conditions
• peano theorem
• fixed point