An initial-boundary problem for a mixed fractional wave equation

Abstract

We aim to prove a unique solvability of an initial-boundary value problem (IBVP) for a time-fractional wave equation in a rectangular domain. We exploit the spectral expansion method as the main tool and used the solution to Cauchy problems for fractional-order differential equations. Moreover, we apply certain properties of the Mittag-Leffler-type functions of single and two variables to prove the uniform convergence of the solution to the considered problem, represented in the form of infinite series.

10 pages

References in corpus (2)

• Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients
• A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators