Existence of a Unique Weak Solution to a Nonlinear Non-Autonomous Time-Fractional Wave Equation (of Distributed-Order)

Karel Van Bockstal
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Karel Van Bockstal: Research Group NaM 2 , Department of Electronics and Information systems, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium

Mathematics, 2020, vol. 8, issue 8, 1-16

Abstract: We study an initial-boundary value problem for a fractional wave equation of time distributed-order with a nonlinear source term. The coefficients of the second order differential operator are dependent on the spatial and time variables. We show the existence of a unique weak solution to the problem under low regularity assumptions on the data, which includes weakly singular solutions in the class of admissible problems. A similar result holds true for the fractional wave equation with Caputo fractional derivative.

Keywords: time-fractional wave equation; distributed-order; non-autonomous; time discretization; existence; uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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