Journal article
Power series solution for fractal differential equations: Power series solution for fractal differential
Bollettino della Unione matematica italiana (2008), Vol.18(2), pp.595-613
06/2025
DOI: 10.1007/s40574-024-00432-9
Abstract
In this paper, we provide an overview of fractal calculus as applied to fractal sets. We introduce the concept of power series defined on fractal sets and explore series solutions for second
α
-order fractal linear differential equations, particularly focusing on solutions near ordinary points. We also investigate the radius of convergence for these fractal series, elucidating the region where these series representations are valid. Furthermore, we employ the fractal Frobenius method to derive series solutions for second
α
-order linear fractal differential equations near regular singular points. By utilizing this method, we obtain analytical expressions that are applicable in the vicinity of such singularities, enhancing our understanding of fractal differential equations. To illustrate our findings, we graphically represent these solutions, providing visual demonstrations of the outcomes. These graphs serve to complement our analytical results and offer insights into the behavior of solutions within the context of fractal calculus and differential equations on fractal sets.
Details
- Title: Subtitle
- Power series solution for fractal differential equations: Power series solution for fractal differential
- Creators
- Alireza Khalili Golmankhaneh - Islamic Azad University, TehranDonatella Bongiorno - University of PalermoHajer Jebali - University of MonastirPalle E. T. Jørgensen - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Bollettino della Unione matematica italiana (2008), Vol.18(2), pp.595-613
- DOI
- 10.1007/s40574-024-00432-9
- ISSN
- 1972-6724
- eISSN
- 2198-2759
- Publisher
- Springer International Publishing
- Grant note
- Scientific and Technological Research Council of Turkey (TUBITAK)
This research was completed with the support of the Scientific and Technological Research Council of Turkey (TUBITAK) (2221-Fellowships for Visiting Scientists and Scientists on Sabbatical Leave-2221-2024/2 period) when Alireza Khalili Golmankhaneh was a visiting scholar at Van Yuzuncu Yil University, Van, Turkey.
- Language
- English
- Date published
- 06/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984821352802771
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