On the generalized fractal calculus of variations

Khalili Golmankhaneh A., Cattani C., Park C., Furuichi S.

Research in Mathematical Sciences, vol.13, no.1, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1007/s40687-025-00573-z
  • Journal Name: Research in Mathematical Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Calculus of variations, Dependent variables, Fractal calculus, Fractal sets, Independent variables
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, we provide a brief overview of fractal calculus and present a comprehensive study of the calculus of variations for functionals on fractal sets. We begin by introducing the calculus of variations for functionals with several dependent variables on fractal sets. We then explore the calculus of variations for functionals with several independent variables on fractal sets. Subsequently, we investigate the calculus of variations for functionals with both several independent and dependent variables on fractal sets. Finally, we suggest applications of fractal calculus of variations in physics, providing examples and plots to illustrate the details.