Year: 2026
Type: article
Abstract: This paper focuses on the Caputo-Hadamard fractional uncertain differential equations (CH-FUDEs) governed by Liu processes, which combine the Caputo–Hadamard fractional derivative with uncertain differential equations to describe dynamic systems involving memory characteristics and uncertain information. Within the framework of uncertain theory, this Liu process serves as the counterpart to Brownian motion. We establish some new Bihari type fractional inequalities that are easy to apply in practice and can be considered as a more general tool in some situations. As applications of those inequalities, we establish the well-posedness of a proposed class of equations under specified non-Lipschitz conditions. Building upon this result, we establish the notions of stability in distribution and stability in measure solutions to CH-FUDEs, deriving sufficient conditions to ensure these stability properties. Finally, the theoretical findings are verified through two numerical examples.
Source: Fractal and Fractional
Authors: Shida Peng, Zhi Li, Jun Zhang, Yuncong Zhu, Liping Xu
Institution: Yangtze University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
OpenAlex ID: W7123363420