Browsing by Author "Vidovic, Zoran"

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Fractal Hankel Transform
(Mdpi, 2025) Golmankhaneh, Alireza Khalili; Sevli, Hamdullah; Cattani, Carlo; Vidovic, Zoran
This paper explores the extension of classical transforms to fractal spaces, focusing on the development and application of the Fractal Hankel Transform. We begin with a concise review of fractal calculus to set the theoretical groundwork. The Fractal Hankel Transform is then introduced, along with its formulation and properties. Applications of this transform are presented to demonstrate its utility and effectiveness in solving problems within fractal spaces. Finally, we conclude by summarizing the key findings and discussing potential future research directions in the field of fractal analysis and transformations.
Fractal Sturm-Liouville Theory
(Mdpi, 2025) Golmankhaneh, Alireza Khalili; Vidovic, Zoran; Tuna, Hueseyin; Allahverdiev, Bilender P.
This paper provides a short summary of fractal calculus and its application to generalized Sturm-Liouville theory. It presents both the fractal homogeneous and non-homogeneous Sturm-Liouville problems and explores the theory's applications in optics. We include examples and graphs to illustrate the effect of fractal support on the solutions and propose new models for fractal structures.
Fractal Telegraph Equation
(Springer int Publ Ag, 2024) Golmankhaneh, Alireza Khalili; Cattani, Carlo; O'Regan, Donal; Tejado, Ines; Vidovic, Zoran
In this paper, we provide a brief review of fractal calculus. We introduce the fractal telegraph equation, which generalizes both the fractal heat and wave equations, and derive its solution. The solutions are plotted to highlight the differences between fractal differential equations and standard differential equations, demonstrating the effects of fractal time and space on the solutions.