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arXiv · 2401.14771

On the separation of solutions to fractional differential equations of order $\alpha \in (1,2)$

Renu Chaudhary·Kai Diethelm·Safoura Hashemishahraki
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Abstract

Given the Caputo-type fractional differential equation $D^\alpha y(t) = f(t, y(t))$ with $\alpha \in (1, 2)$, we consider two distinct solutions $y_1, y_2 \in C[0,T]$ to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference $|y_1(t) - y_2(t)|$ for $t \in [0,T]$. The main emphasis is on describing how such bounds are related to the differences of the associated initial values.

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Renu Chaudhary, Kai Diethelm, Safoura Hashemishahraki. 2024-01-26. On the separation of solutions to fractional differential equations of order $\alpha \in (1,2)$. https://doi.org/10.1016/j.apnum.2024.05.020

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