Perpustakaan Digital ITB

The C ?-Calculus includes functions on fractal sets, which are not differentiable or inte- grable using ordinary calculus. Sumudu transforms have an important role in control en- gineering problems because of preserving units, the scaling property of domains, easy vi- sualization, and transforming linear differential equations to algebraic equations that can be easily solved. Analogues of the Laplace and Sumudu transforms in C ?-Calculus are de- fined 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.