On the Lipschitz condition in the fractal calculus

Alireza K. Golmankhaneh and Cemil Tunc

Chaos, Solitons & Fractals, 2017, vol. 95, issue C, 140-147

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.

Keywords: Fractal calculus; Triadic Cantor set; Fractal Picard iteration; Fractal metric space; Fractal Cauchy sequence (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:95:y:2017:i:c:p:140-147

DOI: 10.1016/j.chaos.2016.12.001

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