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Title: Regularity of solutions to space–time fractional wave equations: A PDE approach
Abstract We consider an evolution equation involving the fractional powers, of order s ∈ (0, 1), of a symmetric and uniformly elliptic second order operator and Caputo fractional time derivative of order γ ∈ (1, 2]. Since it has been shown useful for the design of numerical techniques for related problems, we also consider a quasi–stationary elliptic problem that comes from the realization of the spatial fractional diffusion as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi–infinite cylinder. We provide existence and uniqueness results together with energy estimates for both problems. In addition, we derive regularity estimates both in time and space; the time–regularity results show that the usual assumptions made in the numerical analysis literature are problematic.  more » « less
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Author(s) / Creator(s):
Date Published:
Journal Name:
Fractional Calculus and Applied Analysis
Page Range / eLocation ID:
1262 to 1293
Medium: X
Sponsoring Org:
National Science Foundation
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