Existence, regularity and representation of solutions of time fractional wave equations

Date

2017-09-18

Authors

Keyantuo, Valentin
Lizama, Carlos
Warma, Mahamadi

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We study the solvability of the fractional order inhomogeneous Cauchy problem Dαt u(t) = Au(t) + ƒ(t), t > 0, 1 < α ≤ 2, where A is a closed linear operator in some Banach space X and ƒ : [0, ∞) → X a given function. Operator families associated with this problem are defined and their regularity properties are investigated. In the case where A is a generator of a β-times integrated cosine family (Cβ(t)), we derive explicit representations of mild and classical solutions of the above problem in terms of the integrated cosine family. We include applications to elliptic operators with Dirichlet, Neumann or Robin type boundary conditions on Lp-spaces and on the space of continuous functions.

Description

Keywords

Fractional derivative, Subordination principle, Elliptic operator, Integrated cosine family, Dirichlet, Neumann and Robin boundary conditions

Citation

Keyantuo, V., Lizama, C., & Warma, M. (2017). Existence, regularity and representation of solutions of time fractional wave equations. <i>Electronic Journal of Differential Equations, 2017</i>(222), pp. 1-42.

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Attribution 4.0 International

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