Structure of Fractional Spaces Generated by the Difference Operator and Its Applications. (3rd October 2017)

• Record Type: Journal Article
• Authors: Ashyralyev, Allaberen; Tetikoglu, Fatih Sabahattin
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 10(2017)
• Page Start: 1325
• Page End: 1340
• Publication Date: 2017-10-03
• Subjects: Boundary value problem -- fractional space -- green function -- positive operator; 34B27 -- 30E25 -- 35G15 -- 35J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1316999
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In the present paper, the positivity of the second order of approximation of the difference operator approximates the second-order differential operator with nonlocal conditions is established. The equivalence of norms of these fractional spaces generated by this operator and Hölder spaces is proved. In applications, the stability of difference schemes for the approximate solution of the boundary value problem for elliptic differential equations is provided.