Optimal control and bifurcation diagram for a model nonlinear fractional SIRC

• Published in: Alexandria engineering journal Vol. 59; no. 5; pp. 3481 - 3501
• Main Authors: Mahdy, A.M.S., Higazy, M., Gepreel, K.A., El-dahdouh, A.A.A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-10-2020; The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University; Elsevier
• Subjects: 41A28; 65D05; 65H10; 65L20; 65P30; 65P40; Bifurcation space; Fractional optimal control; Graph of signal flow; Lyapunov exponents; Mittag Generalized-Leffler; Phase space; Poincare maps; Simulink system; SIRC fractional model; Fractional optimal control; Simulink system; Poincare maps; Graph of signal flow; 65Z05; Lyapunov exponents; 65D05; 65L20; 65H10; 65P30; Phase space; Mittag Generalized-Leffler; Bifurcation space; SIRC fractional model; 41A28; 65P40
• ISSN: 1110-0168; 1110-0168
• DOI: 10.1016/j.aej.2020.05.028

In this article, the optimal control for nonlinear SIRC model is studied in fractional order using the Caputo fractional derivative. Graph signal flow is given of the model and simulated by Simulink/Matlab which helps in discussing the topological structure of the model. Dynamics of the system versus certain parameters are studied via bifurcation diagrams, Lyapunov exponents and Poincare maps. The existence of a uniformly stable solution is proved after control. The obtained results display the activeness and suitability of the Mittag Generalized-Leffler function method (MGLFM). The approximate solution of the fractional order SIRC model using MGLFM is explained by giving the figures of solutions before and after control. Also, we plot the 3D relationships with different alpha (fractional order) which display the originality and suitability of the results.