Faedo–Galerkin method for impulsive second-order stochastic integro-differential systems. (May 2022) - Kumar, Surendra; Sharma, Paras
Highlights: We consider impulsive second-order stochastic differential systems in a separable Hilbert space X . We use projection operators to restrict the problem on a finite-dimensional subspace. The existence and convergence of estimated solutions 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 solution. An example is also constructed to demonstrate the effectiveness of the obtained results. Abstract: 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.