Stochastic Foundations of the Fractal Schrödinger Equation
| dc.contributor.author | Golmankhaneh, Alireza Khalili | |
| dc.contributor.author | Isayeva, Elmira | |
| dc.date.accessioned | 2026-01-30T18:35:05Z | |
| dc.date.available | 2026-01-30T18:35:05Z | |
| dc.date.issued | 2026 | |
| dc.description.abstract | In this paper, we extend Nelson's stochastic mechanics to a fractal time framework using fractal calculus. By modeling quantum particle motion with fractal stochastic differential equations, we define forward, backward, and osmotic velocities and derive the fractal Fokker-Planck equation. Introducing a fractal complex wave function, we rigorously derive the fractal Schr & ouml;dinger equation, revealing how quantum behavior can emerge from stochastic dynamics in fractal time. | en_US |
| dc.identifier.doi | 10.1007/s10773-026-06250-3 | |
| dc.identifier.issn | 0020-7748 | |
| dc.identifier.issn | 1572-9575 | |
| dc.identifier.uri | https://doi.org/10.1007/s10773-026-06250-3 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14720/29658 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer/Plenum Publishers | en_US |
| dc.relation.ispartof | International Journal of Theoretical Physics | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Fractal Calculus | en_US |
| dc.subject | Fractal Nelson's Stochastic Mechanics | en_US |
| dc.subject | Fractal Schrödinger Equation | en_US |
| dc.subject | Fractal Stochastic Differential Equations | en_US |
| dc.title | Stochastic Foundations of the Fractal Schrödinger Equation | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication | |
| gdc.description.department | T.C. Van Yüzüncü Yıl Üniversitesi | en_US |
| gdc.description.departmenttemp | [Golmankhaneh, Alireza Khalili] Islamic Azad Univ, Dept Phys, Ur C, Orumiyeh 63896, West Azerbaijan, Iran; [Golmankhaneh, Alireza Khalili] Van Yuzuncu Yil Univ, Fac Sci, Dept Math, Campus, TR-65080 Van, Turkiye; [Isayeva, Elmira] Minist Sci & Educ Republ Azerbaijan, Inst Phys, AZ-1143 Baku, Azerbaijan | en_US |
| gdc.description.issue | 2 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q2 | |
| gdc.description.volume | 65 | en_US |
| gdc.description.woscitationindex | Science Citation Index Expanded | |
| gdc.description.wosquality | Q3 | |
| gdc.identifier.wos | WOS:001664422500001 | |
| gdc.index.type | WoS |