An initial-boundary problem for a mixed fractional wave equation

2025/02/17 by Karimov, Erkinjon, Al-Salti, Nasser, Al-Ghabsi, Muna
#35M10 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.11871

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.

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