An initial-boundary problem for a mixed fractional wave equation

TL;DR

This paper establishes the unique solvability of a mixed fractional wave equation IBVP using spectral expansion and Mittag-Leffler functions, contributing to the mathematical understanding of fractional wave equations.

Contribution

It introduces a novel approach combining spectral expansion and Mittag-Leffler functions to prove solvability of fractional wave equations.

Findings

Proved unique solvability of the fractional wave IBVP.

Demonstrated uniform convergence of the solution series.

Applied spectral methods to fractional differential equations.

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.