https://doi.org/10.1140/epjp/s13360-022-03099-3
Regular Article
The 
-deformed entropic Lagrangians, Hamiltonian dynamics and their applications
Department of Mathematics, Khalifa University of Science and Technology, Zone-1, Main Campus, Abu Dhabi, United Arab Emirates
Received:
21
March
2022
Accepted:
19
July
2022
Published online:
17
August
2022
This is a sequel to our previous paper (Guha in Phys J Plus 137:64, 2022) on Calogero–Leyvraz’s method to study the dynamics of a charged particle moving in a plane under the combined influence of a magnetic field as well as a frictional force. In this paper we modify Calogero–Leyvraz’s entropic kinetic energy term using - deformed logarithm introduced by Tsallis and Kaniadakis to study generalized rate equation. We also derive new kind of fractional damped Liénard type equation which satisfies Chiellini integrability condition. Using deformed Legendre transformation we map the -deformed entropic Lagrangian to deformed Hamiltonian of Calogero–Leyvraz type. We study Hamiltonian mechanics using -deformed Hamiltonian, where the kinetic part is given by the - deformed exponential series. In particular, we give a Hamiltonian formulation for one parameter time-dependent balanced gain–loss system using -deformed logarithm, this reduces to ordinary balanced gain–loss system when 
. Finally, we demonstrate the connection between -deformed Calogero–Leyvraz Hamiltonian with the -deformed Lambert 
(or Lambert–Kaniadakis) function.
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