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https://doi.org/10.1016/j.jare.2021.06.018 2090-1232/ 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review under responsibility of Cairo University. The fractional derivatives and integrals and their potential uses have earned a great importance, mainly because they have become powerful instruments with more accurate, efficient and successful results in mathematical modelling of several complex phenomena in numerous seemingly diverse and widespread fields of science, engineering and finance. As the fractional dynamical systems grow, mature and develop, it is very important to focus on the most promising novel directions that were worked out based on the novel methods and schemes handed over recently in the field. The key objective of this special issue was to focus on recent advancements and future challenges on the basic foundation and applications of the fractional derivatives and integrals in sciences, finance and engineering.