Loading...
2 results
Search Results
Now showing 1 - 2 of 2
- Fractal calculus on fractal interpolation functionsPublication . Gowrisankar, Arulprakash; Khalili Golmankhaneh, Alireza; Serpa, CristinaIn this paper, fractal calculus, which is called F α -calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non differentiable and non-integrable in the sense of ordinary calculus. Graphical representations of fractal calculus of fractal interpolation functions and Weierstrass functions are presented.
- Fractal Laplace transform: analyzing fractal curvesPublication . Khalili Golmankhaneh, Alireza; Welch, Kerri; Serpa, Cristina; Rodríguez-Lopez, RosanaThe concept of Laplace transform has been extended to fractal curves, enabling the solution of fractal differential equations with constant coefficients. This extension, known as the fractal Laplace transform, is particularly useful for handling inhomogeneous differential equations that involve delta Dirac functions and step functions within the realm of fractal functions. A comprehensive table of essential formulas for the fractal Laplace transform has been compiled to facilitate its application in various scenarios. By utilizing this transformative approach, researchers can now delve into the study of fractal functions and address complex problems involving non-traditional geometries. To illustrate the practicality of the fractal Laplace transform, several examples are provided, showcasing its effectiveness in solving fractal differential equations. This advancement represents a significant augmentation of the classical Laplace transform, tailored to suit the distinctive characteristics of fractal systems and functions.