Browsing by Author "Allahverdiev, Bilender P."

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Fractal Sturm-Liouville Problems
(Taylor & Francis Ltd, 2025) Allahverdiev, Bilender P.; Tuna, Huseyin; Golmankhaneh, Alireza Khalili
In this study, fractal Sturm-Liouville problems are considered. First, minimal and maximal operators corresponding to such problems are defined and a symmetric operator is obtained. Then Green's function is constructed and an eigenfunction expansion theorem is obtained. Finally, some examples are given.
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.
Regular Fractal Dirac Systems
(World Scientific Publ Co Pte Ltd, 2025) Allahverdiev, Bilender P.; Tuna, Huseyin; Golmankhaneh, Alireza Khalili
In this paper, the classical one-dimensional Dirac equation is considered under the framework of fractal calculus. First, the maximal and minimal operators corresponding to the problem are defined. Then the symmetric operator is obtained, the Green's function corresponding to the problem is constructed, and the eigenfunction expansion is given. Finally, some examples are given.