Faedo–Galerkin method for impulsive second-order stochastic integro-differential systems. (May 2022)

• Record Type: Journal Article
• Authors: Kumar, Surendra; Sharma, Paras
• Is Part Of: Chaos, solitons and fractals. Volume 158(2022)
• Publication Date: 2022-05
• Subjects: Stochastic differential equation -- Analytic semigroup -- Cosine family of linear operators -- Mild solution -- Fixed point theory -- Faedo–Galerkin technique; 34A12 -- 34A45 -- 58D25 -- 34G20 -- 34k30 -- 47J35; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.111946
• Languages: English
• ISSNs: 0960-0779

Abstract

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.