ABSTRACT
Since there is a clear correlation between poverty and corruption, mathematicians have been actively researching the concept of poverty and corruption in order to develop the optimal strategy of corruption control. This work aims to develop a mathematical model for the dynamics of poverty and corruption. First, we study and analyze the indicators of corruption and poverty rates by applying the linear model along with the Eviews program during the study period. Then, we present a prediction of poverty rates for 2023 and 2024 using the results of the standard problem-free model. Next, we formulate the model in the frame of Caputo fractional derivatives. Fundamental properties, including equilibrium points, basic reproduction number, and positive solutions of the considered model are obtained using nonlinear analysis. Sufficient conditions for the existence and uniqueness of solutions are studied via using fixed point theory. Numerical analysis is performed by using modified Euler method. Moreover, results about Ulam-Hyers stability are also presented. The aforementioned results are presented graphically. In addition, a comparison with real data and simulated results is also given. Finally, we conclude the work by providing a brief conclusion.
ABSTRACT
In the study, we investigate the numerical investigation of variable viscous dissipation and source of heat or sink in mixed convective stagnation point flow the unsteady non-homogeneous nanofluid under the induced magnetic parameter. Considering similarity conversions, the governing of fundamental boundary of layer non-linear PDEs are transformed to equations of the non-linear differential type that, under appropriate boundary conditions, are numerically solved, and the MATLAB function bvp4c is considered to solve the resulting system. The obtained results are calculated numerically for non-dimensional velocity, temperature, and volume fraction and displayed graphically. Further, numbers of Nusselt and Sherwood and local Skin of friction have been produced and displayed by graphs. A comparison with previous results obtained neglecting the new parameters has been made to show the impact of new external parametes on the phenomneon. The obtained findings agree with those introduced by others if the magnetic field and viscous dissipation are neglected. The results obtained have an important applications in diverse field as chemical engineering, agriculture, medical science, and industries.
ABSTRACT
In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.
