On a New Modification of the Erdelyi-Kober Fractional Derivative

Abstract

In this paper, we introduce a new Caputo-type modification of the Erdelyi-Kober fractional derivative. We pay attention to how to formulate representations of Erdelyi-Kober fractional integral and derivatives operators. Then, some properties of the new modification and relationships with other Erdelyi-Kober fractional derivatives are derived. In addition, a numerical method is presented to deal with fractional differential equations involving the proposed Caputo-type Erdelyi-Kober fractional derivative. We hope the presented method will be widely applied to simulate such fractional models.