Generalizing the Mittag-Leffler Function for Fractional Differentiation and Numerical Computation

Abstract

This work aims to investigate fractional differential equations using the Magnus Gösta Mittag-Leffler (GML) function and compare the finding with convention calculus approaches. It examines the solutions with one, two, and three parameters using the GML function for different values of α, β, and γ. We also test the convergence of the GML function of two parameters and check the validity and the computational time complexity. Moreover, we extend the GML function into three dimensions within the domain of complex variables utilizing numerical computing software. Graphs of the single-parameter GML E α (x), illustrates diverse disintegration rates across various α values, emphasizing dominant asymptotic trends over time periods.