Faedo-Galerkin method for impulsive second-order stochastic integro-differential systems

This paper studies impulsive second-order stochastic differential systems in a separable Hilbert space X. By using the projection operators, we restrict the given problem to a finite-dimensional subspace. The existence and convergence of estimated solutions for the considered problem are investigated via the theories of cosine family and fractional powers of a closed linear operator. We also examine the existence and convergence of the Faedo-Galerkin approximate solutions. At last, we are constructed some examples to demonstrate the effectiveness of the obtained results. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper studies impulsive second-order stochastic differential systems in a separable Hilbert space X. By using projection operators, the given problem is restricted to a finite-dimensional subspace. The existence and convergence of estimated solutions are investigated using the theories of cosine family and fractional powers of a closed linear operator. The existence and convergence of Faedo-Galerkin approximate solutions are also examined. Finally, examples are constructed to demonstrate the effectiveness of the obtained results.