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The motivation of this work is to analyse the nonlinear models and their complex nature with generalized tools associated with material and history-based properties. With the help of well-known and widely used numerical scheme, we study the stimulating behaviours of the financial system in this work. The impact of parameters on price index, rate of interest, investment demand, influence changes and investment cost with respect to saving amount, and the elasticity of commercial markets demand are discussed. The consequences of generalizing the model within the arbitrary order are derived. The existence of the solution for the considered system is presented. This study helps beginner researchers to investigate complex real-world problems and predict the corresponding consequences. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present study is to find the solution for a nonlinear system describing the aggregation process of cellular slime mold by using q -homotopy analysis transform method. The coupled system is considered within the frame of the Caputo fractional operator. We examine three different cases with distinct values of sensitivity function χ ρ = 1 , ρ and ρ 2 to exemplify the efficiency and applicability of the considered scheme. We capture the nature of the obtained results with respect to the fractional order, with distinct initial conditions, and illustrate them using 2D and 3D plots for particular values of the parameters. The considered scheme offers parameters, which help to adjust the convergence region, and we plotted the ℏ-curves to dissipate the effect in the present framework. Moreover, some simulating and important behavior of the considered model using attained results shows the prominence of the hired operator while analyzing the coupled equations and confirms the competence of the projected scheme. [ABSTRACT FROM AUTHOR]

In this study, the nonlinear (2+1)-dimensional generalized breaking soliton system has been studied by introducing an appropriate travelling wave transformation. The model under consideration is integrable with constant coefficients and demonstrates Riemann wave propagation characteristics, it principally transformed into a third-order nonlinear ODE. The reliable and robust method, namely the modified exponential function method, is applied to the nonlinear system for the first time. The main goal is to investigate and obtain some explicitly exact travelling waves, periodic waves, and soliton solutions. The obtained solutions are in the form of exponential functions, trigonometric hyperbolic functions, and combined structures of the trigonometric hyperbolic with logarithmic functions. Furthermore, the obtained solutions are new and significant in revealing the pertinent features of the physical phenomenon. The results have been expressed in several graphs, including two- and three-dimensional plots, for the best visual assessment of the physical significance and dynamic characteristics. The most potent and efficacious tools are the computer software packages we utilize to derive solutions and graphs. [ABSTRACT FROM AUTHOR]