An initial-boundary problem for a mixed fractional wave equation
Analysis of PDEs
2026-05-26 v2
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.
Cite
@article{arxiv.2502.11871,
title = {An initial-boundary problem for a mixed fractional wave equation},
author = {Erkinjon Karimov and Nasser Al-Salti and Muna Al-Ghabsi},
journal= {arXiv preprint arXiv:2502.11871},
year = {2026}
}
Comments
10 pages