Chlamydia infection with vaccination asymptotic for qualitative and chaotic analysis using the generalized fractal fractional operator.

In this work, we solve a system of fractional differential equations utilizing a Mittag-Leffler type kernel through a fractal fractional operator with two fractal and fractional orders. A six-chamber model with a single source of chlamydia is studied using the concept of fractal fractional derivatives with nonsingular and nonlocal fading memory. The fractal fractional model of the Chlamydia system can be solved by using the characteristics of a non-decreasing and compact mapping. A suggested model with the Lipschitz criteria and linear growth is studied both qualitatively and quantitatively, taking into account boundedness, uniqueness, and positive solutions at equilibrium points with Leray-Schauder results under time scale concepts. We examined the framework of local and global stability and insight into Lyapunov function properties for the infectious disease model. Chaos Control will employ the regulate for linear responses approach to stabilize the system following its equilibrium points. This will take into consideration a fractional order framework with a managed design, where solutions are bounded in the feasible domain and have a greater impact at the lower minimum infectious rate. To illustrate the implications of fractional and fractal dimensions with varying interest rate values through simulations with Newton's polynomial method under the Mittag-Lefller kernel. Additionally, a comparative analysis of results is also derived by employing power and exponential decay kernels at various fractional orders.