Research article

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

  • Received: 03 November 2019 Accepted: 11 February 2020 Published: 26 February 2020
  • MSC : 28A78, 28A80, 35B35, 35B40, 81Q35

  • 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-μ 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.

    Citation: Cemil Tunç, Alireza Khalili Golmankhaneh. On stability of a class of second alpha-order fractal differential equations[J]. AIMS Mathematics, 2020, 5(3): 2126-2142. doi: 10.3934/math.2020141

    Related Papers:

  • 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-μ 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.


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