Abstract
A new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.
Highlights
In the early twentieth century, the nonlinear Langevin equation (NLE) was offered by PaulLangevin [1], who was an outstanding French scholar in physics
It is possible to obtain the generalized nonlinear Langevin equation (GNLE) in the context of the Zwanzig-Mori projection operator technique [10] and within the framework of the recurrent relation approach from the equation of motion. It is well-known that this approach is utilized in giving an account of phenomena of dynamic nature, ordinary and anomalous transport in physical, chemical, and even biophysical complex systems [10]
An important characteristics of the GNLE is that it involves an aftereffect function, which is named a memory function
Summary
In the early twentieth century, the nonlinear Langevin equation (NLE) was offered by Paul. It is possible to obtain the GNLE in the context of the Zwanzig-Mori projection operator technique [10] and within the framework of the recurrent relation approach from the equation of motion It is well-known that this approach is utilized in giving an account of phenomena of dynamic nature, ordinary and anomalous (such as anomalous diffusion) transport in physical, chemical, and even biophysical complex systems [10]. Many researchers studied generalized nonlinear Langevin equation with fractional derivative [11,12,13,14,15,16,17,18,19]. Langevin equation was studied by Eab and Lim. In this paper, fractional generalized nonlinear.
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