Mohammed K. A. Kaabar (Mathematical Sciences) will gave  a seminar talk titled, "On Martínez-Kaabar Fractal-Fractional Calculus: Methods & Analysis," on Friday, Nov. 7, 2025, at the Seminar on PDEs and Related Topics at the Department of Mathematical Sciences. In this talk, an overview of the idea of fractional calculus is discussed with all recent research trends and applications. Two definitions (Abu-Shady-Kaabar Fractional Derivative, proposed in 2021, and Martínez-Kaabar Fractal-Fractional Derivative, proposed in 2024) in this innovative calculus are provided. Various theorems, techniques, and examples are given to demonstrate the reliability and efficiency of the proposed definitions/ formulations in comparison with other classical fractional approaches. Future research works and suggestions are mentioned to extend the current work to applications related to data science, artificial intelligence, mathematical physics, engineering sciences, and biological sciences.