Hyers-Ulam Stability on Local Fractal Calculus and Radioactive Decay

Abstract

In this paper, we summarize the local fractal calculus, called F-alpha-calculus, which defines derivatives and integrals of functions with fractal domains of non-integer dimensions, functions for which ordinary calculus fails. Hyers-Ulam stability provides a method to find approximate solutions for equations where the exact solution cannot be found. Here, we generalize Hyers-Ulam stability to be applied to oi-order linear fractal differential equations. The nuclear decay law involving fractal time is suggested, and it is proved to be fractally Hyers-Ulam stable.