This paper is devoted to studying the $-Hilfer fractional snap dynamic system under the $-Riemann–Liouville fractional integral conditions on unbounded domains [a, ¥), a ≥ 0, for the first time. The results concerning the existence and uniqueness, along with the Ulam–Hyers, Ulam–Hyers–Rassias, and semi-Ulam–Hyers–Rassias stabilities, are established in an appropriate special Banach space according to fractional calculus, fixed point theory, and nonlinear analysis. At the end, a numerical example is presented for the interpretation of the main results.
