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

Asadzade J. A., Mahmudov N.

PHYSICA SCRIPTA, vol.99, no.7, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 99 Issue: 7
  • Publication Date: 2024
  • Doi Number: 10.1088/1402-4896/ad5917
  • Journal Name: PHYSICA SCRIPTA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

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 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.