University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20231107Some New Results for the $\mathscr{M}$-Transform Involving the Incomplete $I$-Functions70878310.22130/scma.2023.1990549.1265ENSanjayBhatterDepartment of Mathematics, Malaviya National Institute of Technology Jaipur, India.0000-0003-1717-2178Nishant-Department of Mathematics, Malaviya National Institute of Technology Jaipur, India.0000-0000-0000-0000Sunil DuttPurohitDepartment of HEAS (Mathematics), Rajasthan Technical University, Kota, India.Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.0000-0002-1098-5961Journal Article20230227Integral transformations are crucial for solving a variety of actual issues. The right choice of integral transforms aids in simplifying both integral and differential problems into a solution-friendly algebraic equation. In this paper, $\mathscr{M}$-transform is applied to establish the image formula for the multiplication of a family of polynomials and incomplete $I$-functions. Additionally, we discovered image formulations for a few significant and valuable cases of incomplete $I$-functions. Numerous previously unknown and novel conclusions can be reached by assigning specific values to the parameters involved in the primary conclusions drawn in this study.