Hyers–Ulam stability on local fractal calculus and radioactive decay

In this paper, we summarize the local fractal calculus, called F α -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 α -order linear fractal differential equations. The nuclear decay law involving fractal time is suggested, and it is proved to be fractally Hyers–Ulam stable.