Eigenfunctions of laguerre-type operators and generalized evolution problems

On Generalized Hypercomplex Laguerre-Type Exponentials and Applications

“…The operational approach to the classical Laguerre polynomials as considered by Dattoli, Ricci and colaborators in a series of papers ( [7,8]) is based on the introduction of the so-called Laguerre derivative operator in the form ∂ ∂x x ∂ ∂x acting on the set of ( x k k! ) k≥1 .…”

The centroid of the zeroes of a polynomial via certain Laguerre‐type operators

“…In this section, we present the relationship between different centroids of a general monic polynomial and its image under certain Laguerre‐type operator. The Laguerre derivative (see Bretti and Natalini and Dattoli et al), denoted in the following by D L , is defined by Consider the operator D ( r −1) L := DxDx … DxD , r ≥ 2 (containing ( r −1)‐times x , and r ‐times D ). We have where the Stirling numbers of the second kind, , satisfy the fundamental recurrence relation S ( r , j )= jS ( r −1, j )+ S ( r −1, j −1), S (0,0)=1.…”

“…In this section, we present the relationship between different centroids of a general monic polynomial and its image under certain Laguerre-type operator. The Laguerre derivative (see Bretti and Natalini and Dattoli et al 9,10 ), denoted in the following by D L , is defined by…”

Analytic solutions of fractional integro-differential equations of Volterra type with variable coefficients

“…is also named in literature as the Laguerre derivative ([4]- [5]). It is well known that the eigenfunction of the Laguerre derivative is given by the function .2) i.e.…”

“…First, we consider equations containing Laguerre derivatives [5] and Prabhakar operators. We show the advantage of the operational methods to solve a wide class of integro-differential equations involving the Prabhakar operators.…”