Well-Posedness and Approximation for Nonhomogeneous Fractional Differential Equations. (15th June 2021)

• Record Type: Journal Article
• Authors: Liu, Ru; Piskarev, Sergey
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 6(2021)
• Page Start: 619
• Page End: 643
• Publication Date: 2021-06-15
• Subjects: α-times resolvent family -- discretization methods -- explicit scheme -- fractional Cauchy problem -- implicit scheme -- nonhomogeneous fractional equations; 45L05 -- 65M06 -- 65M12; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1901117
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we consider the well-posedness and approximation for nonhomogeneous fractional differential equations in Banach spaces E . Firstly, we get the necessary and sufficient condition for the well-posedness of nonhomogeneous fractional Cauchy problems in the spaces C 0 β ( [ 0, T ] ; E ) . Secondly, by using implicit difference scheme and explicit difference scheme, we deal with the full discretization of the solutions of nonhomogeneous fractional differential equations in time variables, get the stability of the schemes and the order of convergence.