On a New Modification of the Erdélyi–Kober Fractional Derivative

Abstract

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

Keywords

• fractional integrals and derivatives
• Riemann–Liouville fractional operator
• Caputo fractional operator
• Erdélyi–Kober fractional operator
• predictor–corrector method