International mathematical journal of analysis and its applications
CiteScore 2018: 0.72
SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530
Mathematical Citation Quotient (MCQ) 2018: 0.36
Analysis of fractional diffusion equations of distributed order: Maximum principles and their applications
In this paper, we formulate and prove the weak and strong maximum principles for a general parabolic-type fractional differential operator with the Riemann–Liouville time-fractional derivative of distributed order. The proofs of the maximum principles are based on an estimate of the Riemann–Liouville fractional derivative at its maximum point that was recently derived by the authors. Some a priori norm estimates for solutions to initial-boundary value problems for linear and nonlinear fractional diffusion equations of distributed order and uniqueness results for these problems are presented.
Keywords: Riemann–Liouville fractional derivative; distributed-order time-fractional diffusion equation; initial-boundary value problems; maximum principle; uniqueness theorem; stability; linear equation of distributed order; nonlinear equation of distributed order
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