<p>The field of fractional calculus has seen remarkable developments in recent years, accompanied by the application of fractional differential equations in diverse domains such as automatic control theory, biology, and viscoelasticity. These equations offer a more accurate representation of real-world phenomena by considering not only the current state of a system but also its past state and the rate of state change. Functional differential equations, in particular, have found extensive applications in signal recognition, economics, physics, and other fields</p>