On the conformable fractional derivative and its applications in physics
- Laboratoire de Physique Math ´ematique et de Physique Subatomique (LPMPS), Universit ´e Fr `eres Mentouri, Constantine, Algeria
Received: 2024-09-06
Revised: 2024-10-13
Accepted: 2024-10-19
Published 2024-12-30
Copyright (c) -1 Ilyas Haouam (Author)

This work is licensed under a Creative Commons Attribution 4.0 International License.
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Abstract
This research reviews the basics of the conformable fractional derivative (CFD) and explores various applications of it in physics. The conformable fractional versions of path integral approach, divergence and Green’s theorem are thoroughly discussed. Additionally, the basics of Newtonian mechanics in the context of CFD are covered, including velocity, acceleration, Newton's law, Yank, the classical Doppler effect, work, energies and the theory of conservation of momentum. Alongside some fundamentals of special relativity and its postulates are formulated within the frame of CFD, including the Lorentz transformation and fundamental four-vectors. Conformable fractional non-relativistic and relativistic quantum mechanics are also extensively explored, covering the ordinary and angular Schrödinger equations, as well as the Pauli equation. Moreover, a particle-in-a-box model scenario within CFD is investigated, along with the Klein-Gordon, Dirac, and Fisk-Tait equations. Additionally, the continuity equation and a classical limit using Ehrenfest's theorem are derived from the conformable fractional Dirac equation. Some graphics are also included to enhance understanding the behaviors of certain models within CFD, such as the divergence theorem and spherical harmonic.
Keywords
- Conformable fractional derivative,
- Path integra,
- Divergence theorem,
- Classical doppler effec,
- Dirac equatio,
- Conformable fractional quantum mechanic,
- Conformable fractional spherical harmoni,
- Conformable fractional special relativity
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