McLean, William Regularity of solutions to a time-fractional diffusion equation. (English) Zbl 1228.35266 ANZIAM J. 52, No. 2, 123-138 (2010). Summary: We prove estimates for the partial derivatives of the solution to a time-fractional diffusion equation posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is typically less regular than in the familiar case of classical diffusion. Cited in 94 Documents MSC: 35R11 Fractional partial differential equations 35B65 Smoothness and regularity of solutions to PDEs 35C15 Integral representations of solutions to PDEs 35C20 Asymptotic expansions of solutions to PDEs Keywords:fractional derivative; Laplace transform; Sobolev space; singular behaviour PDFBibTeX XMLCite \textit{W. McLean}, ANZIAM J. 52, No. 2, 123--138 (2010; Zbl 1228.35266) Full Text: DOI References: [1] DOI: 10.1007/s00211-006-0045-y · Zbl 1111.65113 · doi:10.1007/s00211-006-0045-y [2] DOI: 10.1017/S0334270000007268 · Zbl 0791.65105 · doi:10.1017/S0334270000007268 [3] Henry, Phys. A 276 pp 448– (2000) [4] DOI: 10.1103/PhysRevE.81.021128 · doi:10.1103/PhysRevE.81.021128 [5] Gorenflo, Fract. Calc. Appl. Anal. 5 pp 491– (2002) [6] Triebel, Interpolation theory, function spaces, differential operators (1995) · Zbl 0830.46028 [7] DOI: 10.1103/PhysRevLett.96.098102 · doi:10.1103/PhysRevLett.96.098102 [8] Thomée, Galerkin finite element methods for parabolic problems 1054 (1984) [9] DOI: 10.1007/s11075-008-9258-8 · Zbl 1177.65194 · doi:10.1007/s11075-008-9258-8 [10] Erdelyi, Higher transcendental functions, Volume 3 (1955) [11] DOI: 10.1007/s11075-010-9379-8 · Zbl 1211.65127 · doi:10.1007/s11075-010-9379-8 [12] DOI: 10.1090/S0025-5718-06-01788-1 · Zbl 1090.65147 · doi:10.1090/S0025-5718-06-01788-1 [13] Metzler, Phys. A 278 pp 107– (2000) [14] DOI: 10.1016/S0370-1573(00)00070-3 · Zbl 0984.82032 · doi:10.1016/S0370-1573(00)00070-3 [15] DOI: 10.1093/imanum/drp004 · Zbl 1416.65381 · doi:10.1093/imanum/drp004 [16] Mainardi, Int. J. Differ. Equ. (2010) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.