mellin-sumudu synergy: a novel paradigm for extending mittag-leffler function

This study presents an innovative reconfiguration of the mittag-leffler function (mlf) by synergistically combining the mellin transform and the sumudu transform. although the mlf plays a significant role in fractional calculus, its complexity has limited its applicability. by utilizing both the mellin and sumudu transforms, new integral representations of the mlf are derived, effectively broadening its scope in addressing fractional differential equations. this integrated approach provides a deeper understanding of the mlf's properties and enables its extension to a wider range of problems in physics, engineering, and mathematics. the effectiveness of the proposed extension is demonstrated through its application to fractional calculus problems, thereby contributing to the advancement of the field and enhancing its ability to model complex real-world phenomena with greater accuracy.