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arXiv · 2401.15407

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

Javad A. Asadzade·Nazim I. Mahmudov
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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.

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Javad A. Asadzade, Nazim I. Mahmudov. 2024-01-27. Euler-Maruyama approximation for stochastic fractional neutral integro-differential equations with weakly singular kernel. https://doi.org/10.1088/1402-4896%2Fad5917

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