Sumudu transform in fractal calculus

Alireza K. Golmankhaneh and Cemil Tunç

Applied Mathematics and Computation, 2019, vol. 350, issue C, 386-401

Abstract: The Cη-Calculus includes functions on fractal sets, which are not differentiable or integrable using ordinary calculus. Sumudu transforms have an important role in control engineering problems because of preserving units, the scaling property of domains, easy visualization, and transforming linear differential equations to algebraic equations that can be easily solved. Analogues of the Laplace and Sumudu transforms in Cη-Calculus are defined and the corresponding theorems are proved. The generalized Laplace and Sumudu transforms involve functions with totally disconnected fractal sets in the real line. Linear differential equations on Cantor-like sets are solved utilizing fractal Sumudu transforms. The results are summarized in tables and figures. Illustrative examples are solved to give more details.

Keywords: Fractal calculus; Staircase function; Cantor-like sets; Fractal Sumudu transform; Fractal Laplace transform (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:350:y:2019:i:c:p:386-401

DOI: 10.1016/j.amc.2019.01.025

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