# On the Laguerre fractional integro-differentiation

### INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS

#### Article

A fractional power interpretation of the Laguerre derivative(DxD)(alpha),D equivalent to d/dx is discussed. The corresponding fractional integrals are introduced. Mapping and semigroup properties, integral representations and Mellin transform analysis are presented. A relationship with the Riemann-Liouville fractional integrals is demonstrated. Finally, a second kind integral equation of the Volterra type, involving the Laguerre fractional integral is solved in terms of the double hypergeometric type series as the resolvent kernel.

### Publication

Year of publication: 2020

### Identifiers

ISSN: 1065-2469

Other: 2-s2.0-85088093895