Least squares finite-element solution of a fractional order two-point boundary value problem

• Published in: Computers & mathematics with applications (1987) Vol. 48; no. 7; pp. 1017 - 1033
• Main Authors: Fix, G.J., Roof, J.P.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2004
• Subjects: Fractional differential operators; Fractional diffusion equations; Least squares finite-element methods; Fractional diffusion equations; Fractional differential operators; Least squares finite-element methods
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2004.10.003

In this paper, a theoretical framework for the least squares finite-element approximation of a fractional order differential equation is presented. Mapping properties for fractional dimensional operators on suitable fractional dimensional spaces are established. Using these properties existence and uniqueness of the least squares approximation is proven. Optimal error estimates are proven for piecewise linear trial elements. Numerical results are included which confirm the theoretical results.