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Some Types of Carathéodory Scheme for Caputo Stochastic Fractional Differential Equations in $L^{p}$ Spaces

$icon-email$ 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 $α \in (\frac{1}{2}, 1)$ 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.

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Some Types of Carathéodory Scheme for Caputo Stochastic Fractional Differential Equations in Lp Spaces

Abstract

Some Types of Carathéodory Scheme for Caputo Stochastic Fractional Differential Equations in $L^{p}$ Spaces