to Fractional Calculus.- Functions Used in Fractional Calculus.- Observation of Fractional Calculus in Physical System Description.- Concept of Fractional Divergence and Fractional Curl.- Fractional Differintegrations: Insight Concepts.- Initialized Differintegrals and Generalized Calculus.- Generalized Laplace Transform for Fractional Differintegrals.- Application of Generalized Fractional Calculus in Electrical Circuit Analysis.- Application of Generalized Fractional Calculus in Other Science and Engineering Fields.- System Order Identification and Control.