On a new generalized local fractal derivative operator

Rami Ahmad El-Nabulsi, Alireza Khalili Golmankhaneh and Praveen Agarwal

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

Abstract: In this study, a new generalized local fractal derivative operator is introduced and we discuss its implications in classical systems through the Lagrangian and Hamiltonian formalisms. The variational approach has been proved to be practical to describe dissipative dynamical systems. Besides, the Hamiltonian formalism is characterized by the emergence of auxiliary constraints free from Dirac auxiliary functions. In field theory, it was found that both damped Klein-Gordon and Dirac equations are generalized, and for specific parameters, a field equation comparable to the Barut equation describing the electromagnetic interactions between N spin-1/2 particles in lepton physics is obtained. A Hamiltonian formulation of higher-order Lagrangian has been constructed and discussed as well. The reformulation of the problem based on fractal calculus has been also addressed in details and compared with the basic approach.

Keywords: Generalized derivative operator; Fractal calculus; The nonlocal classical mechanics; Fractal time; Generalized local fractal derivative operator (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005392

DOI: 10.1016/j.chaos.2022.112329

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