A Chebyshev Spectral Analysis of a Novel Nonlinear Fractional Volterra Dynamical System with Memory Effects and Stability Investigation
DOI:
https://doi.org/10.26713/cma.v17i3.3754Keywords:
Nonlinear fractional dynamical system, Volterra memory standard kernel, Atangana-Baleanu fractional derived model, Chebyshev spectral approach, Fixed point theorem.Abstract
This study uses the Atanjana-Baleanu-Caputo (ABC) operator to give a nonlinear coupled
fractional dynamical that is appropriate with Volterra memory effects. An intricate system with nonlocal
dynamics is calculated using the generalized fractional model with nonlinear interactions. The objective is to
present a novel spectral technique that uses the effects of the Atanjana-Baleanu integral (ABC) operator to
transform the system into a nonlinear Volterra integral equation. Additionally, the fixed point theorem will
be used to determine the existence and uniqueness of the solution under particular conditions. Moreover, we
use Chebyshev spectral inequality to examine the Mittag-Leffler and nonlinear fractional energy stability in
order to approximate analytical solution. The resulting numerical scheme demonstrates the accuracy and
superiority of the suggested spectral framework.
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