Integral transforms and probability distributions for a certain class of Fox-Wright type functions and its applications

Main focus of this paper is to introduce a new class of Fox-Wright type functions and obtain several new integral representations and various integral transforms such as Mellin transform, Whittaker transform, Jacobi transform, Gegenbauer transform, Laplace transform, Euler (Beta) transform, P-delta, R-nu and Hankel transform. Moreover, a new probability density function is also introduced and several properties are studied. As application, fractional derivative and fractional integration formula are established. The results obtained in this paper, are presumably new and their importance is illustrated by several interesting consequences and examples. Furthermore, numerical computation and graphical representations have been expressed to validate the results. (C) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.