INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
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.
Year of publication: 2020