 Maximum principle for the multi-term time-fractional diffusion equations with the Riemann–Liouville fractional derivativesMohammed Al-Refai and Yuri Luchko Applied Mathematics and Computation, 2015, vol. 257, issue C, 40-51 Abstract: In this paper, the initial-boundary-value problems for linear and non-linear multi-term fractional diffusion equations with the Riemann–Liouville time-fractional derivatives are considered. To guarantee the uniqueness of solutions, we employ the weak and the strong maximum principles for the equations under consideration that are formulated and proved in this paper for the first time. An essential element of our proof of the maximum principles is an estimation for the value of the Riemann–Liouville fractional derivative of a function at its maximum point that is established in this paper for a wider space of functions compared to those used in our previous publications. In the linear case, the solutions to the problems under consideration are constructed in form of the Fourier series with respect to the eigenfunctions of the corresponding eigenvalue problems. Keywords: Riemann–Liouville fractional derivative; Extremum principle for the Riemann–Liouville fractional derivative; Maximum principle; Linear and non-linear multi-term time-fractional diffusion equations; Uniqueness and existence of solutions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:40-51 DOI: 10.1016/j.amc.2014.12.127 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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