Abstract
•Different solutions for wave equations are obtained via separation of variables method and the Laplace transform.•Classical, damped and damped with source term fractional wave equations were solved.•Graphical representations are obtained for particular cases shown temporal fractality at different scales.
Analytical solutions of the fractional wave equation via Caputo-Fabrizio fractional derivative are presented in this paper. For this analysis, three cases are considered, the classical, the damped and the damped with a source term defined by fractional wave equations. We show that these solutions are special cases of the time fractional equations with exponential law. Illustrative examples are presented.