Solvability of a <i>ϱ</i>-Hilfer Fractional Snap Dynamic System on Unbounded Domains

Abstract

This paper is devoted to studying the ϱ-Hilfer fractional snap dynamic system under the ϱ-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.

Keywords

• ϱ-Hilfer fractional derivatives
• snap system
• fixed point theorems
• Ulam–Hyers–Rassias stability