On the Lipschitz condition in the fractal calculus

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• 作者：Alireza K. Golmankhaneh ; ^a ; ^{alirezakhalkili2002@yahoo.co.in} ; ^{alirezakhalili2002@yahoo.co.in} ; Cemil Tunc^b ; ^{cemtunc@yahoo.com}
• 关键词：Fractal calculus ; Triadic Cantor set ; Fractal Picard iteration ; Fractal metric space ; Fractal Cauchy sequence
• 刊名：Chaos, Solitons & Fractals
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：95
• 期：Complete
• 页码：140-147
• 全文大小：913 K
• 卷排序：95

文摘

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.