Since the last century, some researchers have focused on the problem of stability of some different differential equations. Stability calculations are made using computer programs today. This has occasionally led to some calculation errors, the exact cause of which is not clear, due to technical details. The purpose of this study is to investigate and classify the stability of individual fractional differential equations. To achieve this goal, computer programs, optimization processes and literature are used. In this way, new algorithmic-theoretical techniques and singular fractional differential equations and new operators are developed and classes are created.