MMN-4985
Existence and stability of solutions for Caputo fractional differential equation through Bielecki metric
Zhuohao Li; Kui Liu;Abstract
In this paper, we have shown that, by considering the Caputo fractional differential equation and Bielecki norm, the existence and uniqueness of solution for Cauchy problem is established using Banach fixed point theorem and further demonstrate the existence of solution without the Lipschitz condition utilizing the Schauder fixed point theorem. Furthermore, under the condition of existence and uniqueness of solution for Caputo fractional differential equation, we present some results about the error estimation, local approximation of solutions and the Ulam-Hyers-Rassias stability. Finally, we provide a numerical example to verify the theoretical results about error estimation.
Vol. 26 (2025), No. 2, pp. 941-953