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A model for speed control in Direct Current (DC) motors has been developed by creating various simulation models grounded in Proportional Integral Derivative (PID) controllers, utilizing the fractional-ordered Adams–Bashforth–Moulton (ABM) method. To achieve a deeper, more effective understanding, a universal closed-loop structure for PID-type controllers has been designed, along with its practical implementation. The PID control framework incorporates a set of rules necessary for tracking diverse environmental parameters. Implementing Fractional-order Control (FOC) in real-world applications requires approaches that enable controller design and parameter tuning for precise, reliable performance. Since conventional PID controllers are sensitive to uncertainties arising from imprecise knowledge of kinematics and dynamics, an Adaptive Fractional PID (AFPID) controller is proposed here to leverage the inherent robustness of fractional-order controllers. While earlier studies treated FPID controller parameters as fixed throughout the control process, this work introduces online parameter adaptation to achieve superior performance. The obtained results demonstrate consistency and mark an advancement in elucidating the connection between chaotic behavior and fractional calculus. It has been found that PI^η D^λ control configurations can significantly enhance controller effectiveness by providing additional tuning parameters. Moreover, initialization and execution times have been markedly reduced, dropping from 2.64 to 0.87 seconds and from 0.5 to 0.15 seconds, respectively.