Rodrigues, M. M.Ferreira, M.Vieira, N.2024-06-202024-06-202024-06-07M. M. Rodrigues, M. Ferreira, and N. Vieira, Distributed-order relaxation-oscillation equation, International Conference of Numerical Analysis and Applied Mathematics 2022 (ICNAAM 2022), Heraklion, Greece, AIP Conference Proceedings 3094(1), 260001 (2024).0094-243Xhttp://hdl.handle.net/10400.8/9727Acknowledgments The work of the authors was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within projects UIDB/04106/2020 and UIDP/04106/2020. N. Vieira was also supported by FCT via the 2018 FCT program of Stimulus of Scientific Employment - Individual Support (Ref: CEECIND/01131/2018).In this short paper, we study the Cauchy problem associated with the forced time-fractional relaxation-oscillation equation with distributed order. We employ the Laplace transform technique to derive the solution. Additionally, for the scenario without external forcing, we focus on density functions characterized by a single order, demonstrating that under these conditions, the solution can be expressed using two-parameter Mittag-Leffler functions.engTime-fractional relaxation-oscillation equationDistributed orderLaplace transformjournal articlehttps://doi.org/10.1063/5.02131991551-7616