Novel comparative analysis of fractional-order partial differential
differential equations arising in quantum field theory pertaining to
Caputo-Fabrizio derivative operator
Abstract
In this paper, we use the $\tilde{q}$-homotopy
analysis transform method ($\tilde{q}$-HATM) to
investigate the explicit solutions of the Kundu-Eckhaus equation and the
massive Thirring model. Kundu-Eckhaus equation is a nonlinear partial
differential equation found in quantum field theory, weakly nonlinear
dispersive water waves, and nonlinear optics, as well as massive
Thirring model, an exactly solvable quantum field theory that defines
the self-interactions of a Dirac field in $(1+1)$ dimensions. The
presented method combines the Yang transform methodology with the
$\tilde{q}$-homotopy analysis technique and the
fractional derivative described by the Caputo-Fabrizio (CF) operator in
an intriguing way. The fixed point postulate is addressed in an attempt
to illustrate that the resulting solution for the presented fractional
order framework exists and is unique. We assess the predicted framework
in the context of fractional order reinforcement and exhibit the
performance of the prospective approach. The physical performance of the
$\tilde{q}$-HATM solutions is also depicted using
graphs for various fractional orders and simulation techniques.The
present study demonstrated that the potential strategy is simple to
apply and very systematic, productive, and precise in analyzing the
behaviour of non-linear PDEs of fractional order that emerge in
engineering and quantum field theory.