General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems

• Published in: Fractional calculus & applied analysis Vol. 19; no. 3; pp. 676 - 695
• Main Authors: Luchko, Yuri, Yamamoto, Masahiro
• Format: Journal Article
• Language: English
• Published: Warsaw Versita 01.06.2016; De Gruyter
• Subjects: 35B30; 35B50; 35C05; 35E05; 35L05; 45K05; 60E99; a priori estimates; Abstract Harmonic Analysis; Analysis; Fourier method of variables separation; Functional Analysis; general fractional derivative; general time-fractional diffusion equation; generalized solution; initial-boundary-value problems; Integral Transforms; Mathematics; maximum principle; Operational Calculus; Primary 26A33; Research Paper; Secondary 35A05; 35C05; Fourier method of variables separation; general fractional derivative; Primary 26A33; 60E99; general time-fractional diffusion equation; initial-boundary-value problems; 35L05; Secondary 35A05; maximum principle; 35E05; a priori estimates; 35B30; 45K05; 35B50; generalized solution

In this paper, we deal with the initial-boundary-value problems for a general time-fractional diffusion equation which generalizes the single- and the multi-term time-fractional diffusion equations as well as the time-fractional diffusion equation of the distributed order. First, important estimates...