On a New Modification of the Erdélyi–Kober Fractional Derivative

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.