New existence and uniqueness result for fractional Bagley-Torvik differential equation

Inspired by the paper of Fazli and Nieto in [Open Math. 17 (2019) 499–512], we establish new existence uniqueness result for a type fractional Bagley–Torvik differential equation. Reported not only generalizes previous results but also adopts different technique. We finish this study concluding remarks which discuss preference our theorem compared to results. An example is constructed with specific parameters that requires weaker conditions unique solution. Meanwhile, construct an iterative sequence converges solution can be commented via Nieto.