Hyers-Ulam stability on local fractal calculus and radioactive decay


Golmankhaneh A. K., Tunç C., Şevli H.

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, vol.230, no.21-22, pp.3889-3894, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 230 Issue: 21-22
  • Publication Date: 2021
  • Doi Number: 10.1140/epjs/s11734-021-00316-5
  • Journal Name: EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC
  • Page Numbers: pp.3889-3894
  • Van Yüzüncü Yıl University Affiliated: Yes

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.