Sumudu transform in fractal calculus

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.

• Publication year

  2019

• Venue

  Applied Mathematics and Computation

• Publication date

  2019-06-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/j.amc.2019.01.025
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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