Dirac Factorization, Partial/Ordinary Differential Equations and Fractional Calculus

The Dirac factorization method (DFM) is the key feature of the present investigation. It is addressed to the relevant use in diverse fields of research, regarding, e.g., the handling of pseudo-operators arising in quantum mechanics and fractional calculus. We explore the role that the factorization plays in a classical context too, including the study of d’Alembert and Laplace equations. Its strong entanglement with the Cauchy–Riemann conditions and with complex analysis is discussed. We complete our study with the extension of DFM to second-order ordinary differential equations, to classical analytical mechanics, and to higher-order partial differential equations.