Well-posedness and regularity of Caputo-Hadamard fractional stochastic differential equations
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.
Caputo-Hadamard fractional stochastic differential equation
scientific article; zbMATH DE number 7363490
scientific article