<p>This paper first analyzes the different types of stability of a generalized class of fractional differential equations (FDEs) involving the new generalized Hattaf mixed (GHM) fractional derivative, which includes numerous forms of fractional operators with both singular and non-singular kernels. This analysis extends and generalizes many existing results related to stability, asymptotic stability and Mittag-Leffler stability reported in previous studies. In addition, the paper develops a novel method for numerically solving FDEs with the GHM fractional derivative. The developed numerical method encompasses the generalized fractional Euler method for initial value problems involving the Caputo fractional derivative, as well as the classical Euler scheme for ordinary differential equations (ODEs). Furthermore, the numerical and analytical results are applied to real-world systems derived from health sciences.</p>