"On the Generalized (k,r)-Fractional Derivative" by Daniela S. Oliveira and Edmundo Capelas de Oliveira

Progress in Fractional Differentiation & Applications

Article Title

On the Generalized (k,r)-Fractional Derivative

Authors

Daniela S. Oliveira, Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing - University of Campinas, 13083- 859, Campinas, SP, BrazilFollow
Edmundo Capelas de Oliveira

Author Country (or Countries)

Brazil

Abstract

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)

http://dx.doi.org/10.18576/pfda/040207

Recommended Citation

S. Oliveira, Daniela and Capelas de Oliveira, Edmundo (2018) "On the Generalized (k,r)-Fractional Derivative," Progress in Fractional Differentiation & Applications: Vol. 4: Iss. 2, Article 7.
DOI: http://dx.doi.org/10.18576/pfda/040207
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol4/iss2/7

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