https://doi.org/10.1140/epjs/s11734-021-00316-5
Regular Article
Hyers–Ulam stability on local fractal calculus and radioactive decay
1
Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran
2
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, 65080, Van, Turkey
3
Department of Computer Engineering, Faculty of Engineering, Van Yuzuncu Yil University, Campus, 65080, Van, Turkey
a a.khalili@iaurmia.ac.ir, alirezakhalili2005@gmail.com
Received:
9
June
2021
Accepted:
25
October
2021
Published online:
9
November
2021
In this paper, we summarize the local fractal calculus, called 
-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 
-order linear fractal differential equations. The nuclear decay law involving fractal time is suggested, and it is proved to be fractally Hyers–Ulam stable.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021
