This book presents a comprehensive investigation into the exponential and Mittag-Leffler Euler differences for semi-linear fractional-order differential equations, a subject falling within the purview of computational mathematics. The field of exponential and Mittag-Leffler Euler differences has witnessed a period of rapid development in recent times. This has led to the emergence of new techniques such as exponential Euler integrator, exponential Runge-Kutta methods, multistep exponential...