Dynamical Characteristics and Signal Flow Graph of Nonlinear Fractional Smoking Mathematical Model

• Published in: Chaos, solitons and fractals Vol. 141; p. 110308
• Main Authors: Mahdy, A.M.S., Mohamed, M.S., Gepreel, K.A., AL-Amiri, A., Higazy, M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2020
• Subjects: Adjacency matrix; Energy of the system; Estrada index; Fractional smoking model; Graph signal flow; RDTM; Reproduction number; Simulink; Stability of equilibrium point; Stability of equilibrium point; Adjacency matrix; Simulink; Energy of the system; RDTM; Estrada index; Reproduction number; 65Z05; Graph signal flow; 65D05; 65L20; 65H10; Fractional smoking model; 65P30; 41A28; 65P40
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2020.110308

•We study analytic solutions for nonlinear fractional smoking model.•We discuss the disease-free equilibrium, stability equilibrium point and number reproduction for the fractional smoking mathematical model.•The signal flow graph and simulink\Matlab of this model are represented simulated.•Results graphical are presented to illustrate the behavior of obtained approximate solutions.•The novelty and significance of the results are clear using a 3D plot. In this article, we study approximate analytic solutions for one of the famous models in biomathematics, namely the nonlinear fractional mathematical smoking model. When alpha=1, we deduce the analytical solution using the Reduced differential transforms method (RDTM) for the nonlinear ordinary mathematical smoking model. The disease-free equilibrium point, the stability of the equilibrium point, and the reproduction number are all discussed for the fractional mathematical smoking model. We use mathematical software packages such as Mathematica to find more iteration when calculating the approximate solution. Results are presented graphically to illustrate the behavior of the obtained approximate solutions. The system is presented by a proposed novel signal flow graph and simulated via SIMULINK/MATLAB. The graph of signal flow is used to calculate some of the model invariants such as the adjacency matrix, model energy, and Estrada index. Also, the novelty and significance of the results are clear using a 3D plot.