In this paper, we investigate the solvability of fractional differential equations involving the Hilfer fractional derivative. This derivative serves as an interpolation between the Caputo and Riemann–Liouville derivatives, depending on the value of a parameter. Our study extends previous results obtained by G. Bozkurt, D. Albayrak, N. Dernekin (2019), who considered similar equations with the Riemann–Liouville derivative, and earlier work by S.-D. Lin and C.-H. Lu (2013) involving the Caputo derivative. By applying the Laplace transform method, we establish the existence result for the proposed problem.