Transformation Operators for Fractional Order Ordinary Differential Equations and Their Applications

The survey is concerned with triangular transformation operators for fractional order α = n − ε ordinary differential equations. We discuss the existence of transformation operators in the case of holomorphic coefficients. Similarity between such operators and the simplest fractional differentiation D0α is discussed too. Applications to the unique determination of the operator from n spectra of boundary value problems are given. Applications to the completeness property of certain boundary value problems for such equations are considered. © 2020, Springer Nature Switzerland AG.