Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel

Abstract

This manuscript examines the problem of nonlinear stochastic fractional neutral integro-differential equations with weakly singular kernels. Our focus is on obtaining precise estimates to cover all possible cases of Abel-type singular kernels. Initially, we establish the existence, uniqueness, and continuous dependence on the initial value of the true solution, assuming a local Lipschitz condition and linear growth condition. Additionally, we develop the Euler-Maruyama method for the numerical solution of the equation and prove its strong convergence under the same conditions as the well-posedness. Moreover, we determine the accurate convergence rate of this method under global Lipschitz conditions and linear growth conditions.

References in corpus (5)

• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media
• Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
• Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler--Maruyama approximation
• Delayed Gronwall inequality with weakly singular kernel

Cited by in corpus (1)

• Finite Time Stability Analysis for Fractional Stochastic Neutral Delay Differential Equations