THE NOVEL BESSEL--MAITLAND FUNCTION INVOLVING SOME CHARACTERISTIC PROPERTIES AND INTEGRAL TRANSFORMS - Khan, Nabiullah; Sk, Rakibul (TWMS journal of applied and engineering mathematics, 2025)
Inspired by certain recent generalizations of the Bessel-Maitland function in this paper, we introduce a new extension of the Bessel-Maitland function associated with the beta function. Some of its characteristic properties including integral representation, recurrence relation and differentiation formula are investigated. Furthermore, we evaluated some integral transforms such as the Mellin transform, K- transform, Euler transform, Laplace transform and Whittaker transform. In addition, we investigated Riemann-Liouville fractional integrals for this Bessel-Maitland function. Keywords: Bessel--Maitland function, beta function, fractional derivative, Mellin transform, Laplace transform, Whittaker transform. AMS Subject Classification: 33B15, 33C10, 26A33, 35A22, 33C45, 33C15, 33C20.