MIXED PROBLEM FOR THE FRACTIONAL ORDER WAVE PROPAGATION EQUATION

Abstract

This article investigates a mixed boundary value problem for the fractional-order wave propagation equation. Differential equations involving fractional derivatives provide a more accurate description of complex dynamic processes compared to classical wave equations. The mathematical model of the fractional-order wave equation is presented and its physical interpretation is discussed. Based on the given initial and boundary conditions, the existence and uniqueness of the solution to the mixed problem are analyzed. Analytical and numerical solution methods are compared and discussed, and several examples are provided to verify the obtained results. The findings of the study contribute to a deeper understanding of physical processes governed by fractional differential equations and offer a theoretical foundation for their practical modeling. This problem was solved using Fourier's method, one of the most common methods in mathematical physics.