Integral transform with the extended generalized Mittag‐Leffler function

Abstract

The paper is devoted to the study of the integral transform

containing the special function å((á, â) _n ;z) generalizing the Mittag‐Leffler type function in the space £_v,r (1 ≤ r ≤ 8, í ∈ R) of Lebesgue measurable functions on R+ = (0,+8) such that ‖ƒ‖ _v,r < 8, where

Mapping properties such as the boundedness, the range, the representation and the inversion of the considered transform are proved. The results are based on the representation of the considered transform as the H‐transform.

Key words:

• Mittag‐Leffler type function
• spaces of p‐summable functions
• H‐function
• H‐transform