Research PaperNo Access

Department of Mathematics, Faculty of Sciences, Van Yüzüncü Yil University, Van, Campus 65080, Turkey

Department of Physics, Urmia Branch, Islamic Azad University, Urmia 63896, West Azerbaijan, Iran

E-mail Address: alirezakhalili@yyu.edu.tr

E-mail Address: alirezakhalili2002@yahoo.co.in

Corresponding author.

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Carlo Cattani

https://orcid.org/0000-0002-7504-0424

Engineering School (DEIM), University of Tuscia, 01100 Viterbo, Italy

Department of Mathematics and Informatics, Azerbaijan University, Baku AZ1014, Azerbaijan

E-mail Address: cattani@unitus.it

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Roman Pasechnik

https://orcid.org/0000-0003-4231-0149

Department of Physics, Lund University, Sölvegatan 14A, Lund, SE-22362, Sweden

E-mail Address: roman.pasechnik@fysik.lu.se

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Shigeru Furuichi

https://orcid.org/0000-0002-9929-0954

Department of Information Science, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, 1540000, Japan

Department of Mathematics, Saveetha School of Engineering, SIMATS Thandalam, Chennai, 602105, Tamil Nadu, India

E-mail Address: furuichi.shigeru@nihon-u.ac.jp

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, and

Palle E. T. Jorgensen

https://orcid.org/0000-0003-2681-5753

Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA

E-mail Address: palle-jorgensen@uiowa.edu

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https://doi.org/10.1142/S0217732325500014Cited by:0 (Source: Crossref)

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.

Keywords:

PACS: 05.45.Df, 04.20.Fy

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