On stability of a class of second alpha-order fractal differential equations


TUNÇ C. , Golmankhaneh A. K.

AIMS MATHEMATICS, cilt.5, ss.2126-2142, 2020 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 5 Konu: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3934/math.2020141
  • Dergi Adı: AIMS MATHEMATICS
  • Sayfa Sayısı: ss.2126-2142

Özet

In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions that are not differentiable or integrable on totally disconnected fractal sets such as middle-mu Cantor sets. Analogues of the Lyapunov functions and their features are given for asymptotic behaviors of fractal differential equations. The stability of fractal differentials in the sense of Lyapunov is defined. For the suggested fractal differential equations, sufficient conditions for the stability and uniform boundedness and convergence of the solutions are presented and proved. We present examples and graphs for more details of the results.