Fractal calculus of variations for problems with constraints
Alireza Khalili Golmankhaneh, Carlo Cattani, Roman Pasechnik, Shigeru Furuichi, Palle E. T. Jørgensen
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.
Topics & Concepts
PhysicsFractalCalculus (dental)Theoretical physicsStatistical physicsApplied mathematicsMathematical analysisMedicineMathematicsDentistryMathematical and Theoretical AnalysisMathematical Dynamics and FractalsComplex Systems and Time Series Analysis