Discrete Fractional Dynamics and Its Applications

November 23, 9:00-11:00 Am, Central Time 


Fractional sums and differences were introduced in the 90th of the last century. The seminal result is presented in the Miller and Ross’ paper “Fractional Difference Calculus” in Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications, Japan, 1988. The next significant step in the development of discrete fractional calculus (Riemann-Liouville and Caputo) was done in works by Atici and Eloe in the first decade of this century. Among the other things, Atici and Eloe obtained a solution of the initial value problem for a simple fractional difference equation. In 2014 Wu and Baleanu proposed to use this solution to generate fractional difference maps. Fractional universal and standard maps as solutions of the fractional differential equations of kicked systems were introduced in 2008 in a paper by Tarasov and Zaslavsky “Fractional equations of kicked systems and discrete maps” and later fractional logistic map was introduced in 2013 by Edelman. The applications of fractional maps include secure communication, economics, and lifespan of living species. Significant progress in the development and applications to control of the Grünwald–Letnikov fractional differences was done by Ostalczyk with co-authors (see Ostalczyk’s book “Discrete Fractional Calculus”, 2016). Over the last decade many authors, not mentioned here, contributed to the development of the discrete fractional calculus and its applications. The purpose of this symposium is to make an overview of the recent results, to reconcile any differences in notations used by various authors, and to discuss new directions in this emerging field.

Professor Mark Edelman
Yeshiva University, NY, USA

Professor Dumitru Baleanu
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey
Institute of Space Sciences, Magurele-Bucharest, Romania