Linear fractional dynamic equations: Hyers–Ulam stability analysis on time scale

Abstract

The article’s purpose is to examine ăthe Hyers–Ulam stability (HUS) for some linear fractional dynamic equations (FDEs) with the Caputo Δ−derivative on time scale. If we swap out a certain FDE for a fractional dynamical inequality, we want to know how close the solutions of the fractional dynamical inequality are to the solutions of the exact FDEs. Meanwhile, the generalized HUS result is obtained as a direct corollary. To achieve this goal, we solve the aforementioned equations utilizing the time scale version of the Laplace transform. Subsequently, the HUS is investigated in accordance with theseăsolutions.

Keywords

• Time scale
• Time scale Laplace transform
• Linear dynamic equations
• Fractional calculus
• Ulam Stability
• Fractional dynamic equations