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Some Types of Carathéodory Scheme for Caputo Stochastic Fractional Differential Equations in $L^p$ Spaces
Phan Thi Huong
,
Pham The Anh
Abstract
In this paper, we construct Carathéodory type and exponential Carathéodory type schemes for Caputo stochastic fractional differential equations (CSFDEs) of order $\alpha \in (\frac{1}{2},1)$ in $L^p$ spaces with $p \geq 2$ whose coefficients satisfy a standard Lipschitz and a linear growth bound conditions. The strong convergence and the convergence rate of these schemes are also established.