In this study, it is described the general forms of fractional-order differential equations and asymtotic stability of their system's equilibria. In addition that, the stability analysis of equilibrium points of the local bacterial infection model which is fractional-order differential equation system, is made. Results of this analysis are supported via numerical simulations drawn by datas obtained from literature for mycobacterium tuberculosis and the antibiotics isoniazid (INH), rifampicin (RIF), streptomycin (SRT) and pyrazinamide (PRZ) used against this bacterial infection. Anahtar Kelimeler: kesirsel mertebeden diferansiyel denklem sistemi, matematiksel model, kararlılık analizi, denge noktaları, çoklu antibiyotik tedavisi