A new collection of real world applications of fractional calculus in science and engineering

By Hongguang Sun, Yong Zhang, Dumitru Băleanu, Wen Chen, YangQuan Chen. Communications in nonlinear science & numerical simulation, 2018

1,595 citations recorded by the source corpus.

Abstract Fractional calculus is at this stage an arena where many models are still to be introduced, discussed and applied to real world applications in many branches of science and engineering where nonlocality plays a crucial role. Although researchers have already reported many excellent results in several seminal monographs and review articles, there are still a large number of non-local phenomena unexplored and waiting to be discovered. Therefore, year by year, we can discover new aspects of the fractional modeling and applications. This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus. We believe this incomplete, but important, information will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool. We expect this collection will also benefit our community.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6a717162c3232087b3120c88b0c51e3bc69f8e07

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Citations in the corpus

Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation (2019, background): “Later, researchers discovered that fractional derivative has a wide applications in the various fields of natural sciences and engineering such as found in control theory of dynamical systems, signal and image processing, financial modeling, nanotechnology, viscoelasticity, random walk, anomalous tr”
Classes of operators in fractional calculus: A case study (2021, methodology): “Note that it makes sense for both ρ = 1 and ρ = −1 to give the same operators in opposite orders, because under the convention (9), negating both β and ρ (or, in this case of β = 0, just negating ρ) is what swaps the Prabhakar integral with the Prabhakar derivative of Riemann–Liouville type.”
On tempered fractional calculus with respect to functions and the associated fractional differential equations (2021, background): “For broad overviews of these topics, we refer the reader to the well-known textbooks and survey articles such as [1, 2, 3, 4, 5, 6].”
Weighted Fractional Calculus: A General Class of Operators (2022, background): “Such generalisations are not only a pure mathematical curiosity, as differential equations involving the generalised operators have been applied in many scientific fields [4,5] ranging from viscoelasticity [6] to epidemiology [7] to economics [8,9] to electrical circuits [10].”
On a Fractional Operator Combining Proportional and Classical Differintegrals (2020, background): “These have many useful applications due to the non-locality of fractional derivatives: many processes with non-local behaviours can be modelled most efficiently using fractional differential equations [3].”