We generalize a fractional derivative type, the so-called (k,r)-fractional derivative and establish some properties of the resulting generalized operator. As an application we show that with this new definition, the Cauchy problem is equivalent to a Volterra integral equation of the second kind. We discuss, for this problem, some particular cases.
Digital Object Identifier (DOI)
S. Oliveira, Daniela and Capelas de Oliveira, Edmundo
"On the Generalized (k,r)-Fractional Derivative,"
Progress in Fractional Differentiation & Applications: Vol. 4
, Article 7.
Available at: https://dc.naturalspublishing.com/pfda/vol4/iss2/7