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    Population dynamics are influenced by growth and resource consumption, suggesting neutral equations. This study investigates periodic solutions for a generalized Rayleigh-type equation using fractional calculus and state-dependent delay.

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    Area of Science:

    • Population Dynamics
    • Mathematical Biology
    • Fractional Calculus

    Background:

    • Population growth necessitates increased resource consumption, impacting population dynamics.
    • Neutral equations are relevant for modeling populations where resource availability is a factor.
    • Generalized Rayleigh-type equations are used to model oscillatory phenomena.

    Purpose of the Study:

    • To investigate sufficient conditions for the existence of periodic solutions.
    • To analyze a generalized Rayleigh-type equation with state-dependent delay.
    • To apply fractional calculus concepts to population dynamics models.

    Main Methods:

    • Utilizing fractional calculus.
    • Analyzing a generalized Rayleigh-type equation.
    • Incorporating state-dependent delay into the model.

    Main Results:

    • Established sufficient conditions for periodic solutions.
    • Demonstrated the applicability of fractional calculus in this context.
    • Provided insights into the behavior of populations with state-dependent delays.

    Conclusions:

    • The study successfully identified conditions for periodic solutions in the investigated equation.
    • Fractional calculus offers a valuable framework for modeling complex population dynamics.
    • State-dependent delays significantly influence population dynamics and require specific analytical approaches.