Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation.

This work examines the fractional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) by utilizing three well-known analytical methods, the modified [Formula: see text]-expansion method, [Formula: see text]-expansion method and the Kudryashov method. The gKdV-ZK equation is a nonlinear model describing the influence of magnetic field on weak ion-acoustic waves in plasma made up of cool and hot electrons. The kink, singular, anti-kink, periodic, and bright soliton solutions are observed. The effect of the fractional parameter on wave shapes have been analyzed by displaying various graphs for fractional-order values of [Formula: see text]. In addition, we utilize the Hamiltonian property to observe the stability of the attained solution and Galilean transformation for sensitivity analysis. The suggested methods can also be utilized to evaluate the nonlinear models that are being developed in a variety of scientific and technological fields, such as plasma physics. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complex models.

Computational analysis for eccentric neighborhood Zagreb indices and their significance.

In this paper, a novel eccentric neighborhood degree-based topological indices, termed eccentric neighborhood Zagreb indices, have been conceptualized and its discriminating power investigated with regard to the predictability of the boiling point of the chemical substances. The discriminating power of the eccentric neighborhood Zagreb indices was compared with that of Wiener and eccentric connectivity indices. Some explicit results for those new indices for some graphs and graph operations such as join, disjunction, composition, and symmetric difference.