Some New Application of Extended Wright Function

This study introduces a novel extension of the Wright function using the Macdonald function as an extension of the Pochhammer symbol. We establish integral, differential, and generating function formulas for this new function. Furthermore, we apply it to fractional differential equations, providing integral transformations of Cauchy‐type problems with graphical representation. The Mellin and Rishi transformations are also derived for the extended Wright function. These results offer new insights and potential applications in fractional calculus (FC), mathematical physics, and engineering. MSC2020 Classification : 26A33, 33B15, 33C05, 65D20, 33E20, 91B25