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On the Lipschitz condition in the fractal calculus

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  • Golmankhaneh, Alireza K.
  • Tunc, Cemil

Abstract

In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the Fα-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the Fα-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.

Suggested Citation

  • Golmankhaneh, Alireza K. & Tunc, Cemil, 2017. "On the Lipschitz condition in the fractal calculus," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 140-147.
    • Handle: RePEc:eee:chsofr:v:95:y:2017:i:c:p:140-147
    DOI: 10.1016/j.chaos.2016.12.001
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    References listed on IDEAS

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    1. Satin, Seema E. & Parvate, Abhay & Gangal, A.D., 2013. "Fokker–Planck equation on fractal curves," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 30-35.
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    Cited by:

    1. Golmankhaneh, Alireza K. & Tunç, Cemil, 2019. "Sumudu transform in fractal calculus," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 386-401.
    2. Khan, Hasib & Ahmad, Farooq & Tunç, Osman & Idrees, Muhammad, 2022. "On fractal-fractional Covid-19 mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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