Affiliation:
1. Department of Mathematics and Statistics, University of Nevada Reno, NV 89557, USA
2. Department of Mathematics, Sakarya University, 54050, Sakarya, Turkey
Abstract
<p style='text-indent:20px;'>This work establishes the parallel between the properties of classic elliptic PDEs and the one-sided 1-D fractional diffusion equation, that includes the characterization of fractional Sobolev spaces in terms of fractional Riemann-Liouville (R-L) derivatives, variational formulation, maximum principle, Hopf's Lemma, spectral analysis, and theory on the principal eigenvalue and its characterization, etc. As an application, the developed results provide a novel perspective to study the distribution of complex roots of a class of Mittag-Leffler functions and, furthermore, prove the existence of real roots.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Analysis,General Medicine
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