A Comment on a Controversial Issue: A Generalized Fractional Derivative Cannot Have a Regular Kernel

• Published in: Fractional calculus & applied analysis Vol. 23; no. 1; pp. 211 - 223
• Main Author: Hanyga, Andrzej
• Format: Journal Article
• Language: English
• Published: Warsaw Versita 01.02.2020; De Gruyter; Nature Publishing Group
• Subjects: 26A33; 34A99; Abstract Harmonic Analysis; Analysis; Bernstein function; completely monotone function; Derivatives; fractional calculus; Functional Analysis; Integral Transforms; Integrals; Kernels; LICM function; Mathematics; Monotone functions; Operational Calculus; Research Paper; Sonine equation; Stieltjes function; Sonine equation; fractional calculus; Bernstein function; 26A33; 34A99; Stieltjes function; completely monotone function; LICM function

The problem whether a given pair of functions can be used as the kernels of a generalized fractional derivative and the associated generalized fractional integral is reduced to the problem of existence of a solution to the Sonine equation. It is shown for some selected classes of functions that a ne...