An Analysis and Global Identification of Smoothless Variable Order of a Fractional Stochastic Differential Equation

Author:

Li Qiao1,Zheng Xiangcheng2,Wang Hong3,Yang Zhiwei4ORCID,Guo Xu5

Affiliation:

1. School of Engineering Medicine, Beihang University, Beijing 100083, China

2. School of Mathematics, Shandong University, Jinan 250100, China

3. Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA

4. School of Mathematical Sciences, Fudan University, Shanghai 200433, China

5. Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China

Abstract

We establish both the uniqueness and the existence of the solutions to a hidden-memory variable-order fractional stochastic partial differential equation, which models, e.g., the stochastic motion of a Brownian particle within a viscous liquid medium varied with fractal dimensions. We also investigate the inverse problem concerning the observations of the solutions, which eliminates the analytic assumptions on the variable orders in the literature of this topic and theoretically guarantees the reliability of the determination and experimental inference.

Funder

Taishan Scholars Program of Shandong Province of China

National Natural Science Foundation of China

National Science Foundation

Major Fundamental Research Project of Shandong Province of China

China Postdoctoral Science Foundation

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

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