Fractal calculus of variations for problems with constraints
(2025) In Modern Physics Letters A 40(7-8).- Abstract
In this paper, we present a summary of fractal calculus and propose the use of Lagrange multipliers for both fractal calculus and fractal variational calculus with constraints. We examine the application of these methods across various branches of physics. By employing fractal variational calculus with constraints, we derive fundamental equations such as the fractal mechanical wave equation, the fractal Schrödinger equation in quantum mechanics, Maxwell's equations in fractal electromagnetism, and the Lagrange equation for constraints in fractal classical mechanics. Several examples are provided to illustrate these concepts in detail.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/6afb04b9-d1ff-4b2c-87a8-96cb75947fc1
- author
- Golmankhaneh, Alireza Khalili ; Cattani, Carlo ; Pasechnik, Roman LU ; Furuichi, Shigeru and Jorgensen, Palle E.T.
- organization
- publishing date
- 2025-03-14
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- constraints, Fractal calculus, fractal variational calculus, Lagrangian multipliers
- in
- Modern Physics Letters A
- volume
- 40
- issue
- 7-8
- article number
- 2550001
- publisher
- World Scientific Publishing
- external identifiers
-
- scopus:85219126732
- ISSN
- 0217-7323
- DOI
- 10.1142/S0217732325500014
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © World Scientific Publishing Company.
- id
- 6afb04b9-d1ff-4b2c-87a8-96cb75947fc1
- date added to LUP
- 2025-07-04 09:43:34
- date last changed
- 2025-07-07 07:51:19
@article{6afb04b9-d1ff-4b2c-87a8-96cb75947fc1,
abstract = {{<p>In this paper, we present a summary of fractal calculus and propose the use of Lagrange multipliers for both fractal calculus and fractal variational calculus with constraints. We examine the application of these methods across various branches of physics. By employing fractal variational calculus with constraints, we derive fundamental equations such as the fractal mechanical wave equation, the fractal Schrödinger equation in quantum mechanics, Maxwell's equations in fractal electromagnetism, and the Lagrange equation for constraints in fractal classical mechanics. Several examples are provided to illustrate these concepts in detail.</p>}},
author = {{Golmankhaneh, Alireza Khalili and Cattani, Carlo and Pasechnik, Roman and Furuichi, Shigeru and Jorgensen, Palle E.T.}},
issn = {{0217-7323}},
keywords = {{constraints; Fractal calculus; fractal variational calculus; Lagrangian multipliers}},
language = {{eng}},
month = {{03}},
number = {{7-8}},
publisher = {{World Scientific Publishing}},
series = {{Modern Physics Letters A}},
title = {{Fractal calculus of variations for problems with constraints}},
url = {{http://dx.doi.org/10.1142/S0217732325500014}},
doi = {{10.1142/S0217732325500014}},
volume = {{40}},
year = {{2025}},
}