Mittag-Leffler Functions and the Sawi Transform: A New Approach to Fractional Calculus

- This study uses the Sawi transform and Mittag-Leffler function to introduce a novel method of fractional calculus. The basic characteristics of the Sawi transform and its connection to other transforms such as the Laplace transform are explored. We demonstrate the application of the Sawi transform in deriving novel solutions to fractional differential equations and elucidate the importance of the Mittag-Leffler function in these scenarios. We show the efficiency of the presented method by presenting some nonhomogeneous equations and initial value problems. This study proves the efficacy of the Sawi transform by handling some problems in the sense of Caputo fractional calculus.