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This project is dedicated to fractional calculus, one of the most dynamic areas of mathematical science today. For 50 years, the number of researchers and scientific publications dealing with this topic has been increasing day by day, which clearly demonstrates the growing interest in fractional calculus, both from a practical and a theoretical point of view. The purpose of this reprint is to extend existing results in fractional calculus by considering various types of fractional operators, such as Caputo-type, Hilfer-type, and Riemann-Liouville-type, by introducing various types of inequalities, such as Bullen-type, Jensen-Mercer-type, and Hermite-Hadamard-type, as well as by analyzing fractional-order differential equations and boundary value problems.