Regular variation and fractional operators

Článek WoS

en

The paper can be understood as a contribution to the study of relationships between the notion of regular variation on one hand and fractional calculus on the other hand, along with their consequences. We present a full fractional extension of some of the fundamental statements from the theory of regularly varying functions, thereby providing a characterization of regular variation in terms of fractional operators. Various types of fractional integral and differential operators are included. Asymptotics at infinity as well as at the initial point is studied. We also establish new versions of the fractional L'Hospital rule. The obtained results will find applications in the asymptotic theory of fractional differential equations. As a by-product, we obtain information on the solutions to the equations which, in the limiting case, lead to viscoelastic models.

Regular variation, Fractional integral, Fractional derivative, Karamata theorem, Monotone density theorem, L'Hospital rule

2026-04-01

Springer Nature

Fractional Calculus and Applied Analysis

29

2

662–682

21