The chapter "Generalized fractional calculus and applications" delves into the advanced topics of fractional calculus, focusing on generalized operators of fractional integration and differentiation. It begins with definitions and examples of these operators, including the $I_{\beta,m}^{(\gamma_k),(\delta_k)}$-operators, which are integral transforms of convolutional type and compositions of Erdélyi-Kober operators. The chapter also covers the properties of Riemann-Liouville and Weyl type generalized fractional integrals, as well as generalized fractional differentiation operators. Subsequent sections explore recent aspects of classical Erdélyi-Kober operators, including convolutions, Džrbashjan-Gelfond-Leontiev operators, and their commutants. The chapter then introduces hyper-Bessel differential and integral operators, detailing their definitions, projectors, and applications in mathematical physics. It discusses solutions to homogeneous and non-homogeneous hyper-Bessel equations, transmutation methods, and the Obrechkoff integral transform. The final sections apply these concepts to generalized hypergeometric functions, providing Poisson type integral representations and fractional derivative representations. The chapter concludes with further generalizations and applications, including generalized fractional integrals involving Fox's $H$-function, solutions to Abel type integral equations, and applications in univalent function theory. The appendix provides definitions, examples, and properties of special functions used throughout the book.The chapter "Generalized fractional calculus and applications" delves into the advanced topics of fractional calculus, focusing on generalized operators of fractional integration and differentiation. It begins with definitions and examples of these operators, including the $I_{\beta,m}^{(\gamma_k),(\delta_k)}$-operators, which are integral transforms of convolutional type and compositions of Erdélyi-Kober operators. The chapter also covers the properties of Riemann-Liouville and Weyl type generalized fractional integrals, as well as generalized fractional differentiation operators. Subsequent sections explore recent aspects of classical Erdélyi-Kober operators, including convolutions, Džrbashjan-Gelfond-Leontiev operators, and their commutants. The chapter then introduces hyper-Bessel differential and integral operators, detailing their definitions, projectors, and applications in mathematical physics. It discusses solutions to homogeneous and non-homogeneous hyper-Bessel equations, transmutation methods, and the Obrechkoff integral transform. The final sections apply these concepts to generalized hypergeometric functions, providing Poisson type integral representations and fractional derivative representations. The chapter concludes with further generalizations and applications, including generalized fractional integrals involving Fox's $H$-function, solutions to Abel type integral equations, and applications in univalent function theory. The appendix provides definitions, examples, and properties of special functions used throughout the book.