Well-posedness and regularity of Caputo-Hadamard fractional stochastic differential equations
type: Item
instance of: scholarly article
title: Well-posedness and regularity of Caputo-Hadamard fractional stochastic differential equations
zbMATH Open document ID: 1471.34024
author: Zhiwei Yang
author: Xiangcheng Zheng
author: Hong Wang
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2021-06-25T00:00:00Z
review text: This paper focuses primarily on the Caputo-Hadamard fractional stochastic differential equation (SDE) of order \(1/2 <\alpha< 1\) driven by a multiplicative noise, which contains a non-Lipschitz weakly singular logarithmic kernel, and serves as the generalization of the classical SDE \(u^{\prime}(t)=f(u(t))+b(u(t))\frac{dW_{t}}{dt}\) in order to describe the ultraslow diffusion processes of particles. The first few pages introduce all the necessary notation and terminology to understand the paper: present modeling issues and auxiliary results that are used in subsequent analysis. The main results are presented in Section 3 (the well-posedness and moment estimates) and 4 (regularity) through Theorem 3 and 4, respectively. In Section 3, the proof of the existence and uniqueness of the Caputo-Hadamard fractional SDE is studied. Section 4 is devoted to the regularity of the solutions to the proposed model. Section 5 is about concluding remarks.
reviewed by: Arzu Ahmadova
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 7363490
zbMATH Keywords: Caputo-Hadamard fractional stochastic differential equation
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: regularity
MaRDI profile type: Publication
full work available at URL: s00033-021-01566-y
OpenAlex ID: W3175907543
Wikidata QID: Q115389283
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DOI: 10.1007/S00033-021-01566-Y
description: scientific article; zbMATH DE number 7363490