Upper and lower estimates for the separation of solutions to fractional differential equations

Abstract

Given a fractional differential equation of order $\alpha \in (0,1]$ with Caputo derivatives, we investigate in a quantitative sense how the associated solutions depend on their respective initial conditions. Specifically, we look at two solutions $x_1$ and $x_2$, say, of the same differential equation, both of which are assumed to be defined on a common interval $[0,T]$, and provide upper and lower bounds for the difference $x_1(t)-x_2(t)$ for all $t\in [0,T]$ that are stronger than the bounds previously described in the literature.

arXiv comment3 figures

References in corpus (3)

• Trapezoidal methods for fractional differential equations: theoretical and computational aspects
• Generation of nonlocal fractional dynamical systems by fractional differential equations
• Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

Cited by in corpus (2)

• A new approach to shooting methods for terminal value problems of fractional differential equations
• On the separation of solutions to fractional differential equations of order $\alpha \in (1,2)$