An Identity Involving Integration with Respect to Variable Order of Fractional Derivative

Abstract

In 1993, Samko and Ross introduced the study of fractional integration and differentiation when the order is not a constant but a function. This suggestion gave rise to a number of further ideas and results. In particular, this implies a possibility of integration with respect to derivative's order. Here an identity is presented, in which an expression involving Riemann--Liouville fractional derivative is integrated with respect to the derivative's order.