Applications of the generalized gamma function to a fractional-order biological system

In this work, variety of complex dynamics are found in a fractional-order antimicrobial resistance (AMR) model based on the generalized Gamma function. Firstly, extended left and right Caputo fractional differential operators, respectively, ELCFDO ERCFDO introduced. The basic features outlined. is shown to have new parameter that affects occurrence AMR system. Secondly, discretization studied using piecewise constant arguments. Then, discretized version system involving investigated such as existence Neimark–Sacker (NS) flip bifurcations, closed invariant curves (CIC), strange attractors with fractal or multi-fractal structures, chaotic attractors. Finally, an extension fractal-fractional operator (FFO) combines differentiation carried out FFO (EFFO) applied proposed system, which also generates similar dynamics.