Abstract
In this paper, we study the Langevin equation within the generalized proportional fractional derivative. The proposed equation involves a variable coefficient and subjects to mixed integrodifferential boundary conditions. We introduce the generalized proportional fractional derivative and expose some of its features. We mainly investigate the existence, uniqueness and different types of Ulam stability of the solutions via fixed point theorems and inequality techniques. Finally, we provide two examples to support our main results.