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Fractal Laplace transform: analyzing fractal curves
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Orientador(es)
Resumo(s)
The 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.
Descrição
Cristina Serpa acknowledges partial funding by national funds through FCTFoundation for Science and Technology, project reference: UIDB/04561/2020.
Palavras-chave
Fractal calculus Fractal laplace transform Fractal dirac function Fractal curves UIDB/04561/2020
Contexto Educativo
Citação
Golmankhaneh, A. K., Welch, K., Serpa, C., & Rodríguez-Lopez, R. (2023). Fractal Laplace transform: analyzing fractal curves. Journal of Analysis, 32(2), 1111-1137. https://doi.org/10.1007/s41478-023-00677-1
Editora
Springer Nature