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The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the
Autor:
Kai Diethelm
Publikováno v:
Mathematics, Vol 10, Iss 8, p 1245 (2022)
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately evident that the
Externí odkaz:
https://doaj.org/article/1d265dfb9b8d47458ec2e1831b0c897e
Publikováno v:
Mathematics, Vol 8, Iss 3, p 324 (2020)
The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order
Externí odkaz:
https://doaj.org/article/ed2fa7a7fe3e498d9509b655b8420c16
This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar systems and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::66ed5f2b51d8d0889095ade251aab90d
http://arxiv.org/abs/2205.01744
http://arxiv.org/abs/2205.01744
Publikováno v:
Fractional Calculus and Applied Analysis. 23:610-634
In recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non-singular (i.e., bounded) kernel. It will
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9cca28f1ea8a8f7a1c6d02dcdcb84a61
https://doi.org/10.1515/fca-2020-0032
https://doi.org/10.1515/fca-2020-0032
Autor:
Aliaa Burqan, Rania Saadeh, Ahmad Qazza, Osama Yusuf Ababneh, Juan C. Cortés, Kai Diethelm, Dia Zeidan
This book presents a thoughtful compilation of chapters derived from the proceedings of the 8th International Arab Conference on Mathematics and Computations (IACMC 2023), held at Zarqa University in Zarqa, Jordan, from 10–12 May 2023. Encompassing
Autor:
Kai Diethelm
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the fractional
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4b684da9bfce9cf4c912c3e3cbad0c22
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5615dc7a7c38ee4938e8d62d233e1e01
Autor:
Kai Diethelm
Publikováno v:
Encyclopedia of Continuum Mechanics ISBN: 9783662536056
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::50d27c7af8598db63c2e9fc085f351ea
https://doi.org/10.1007/978-3-662-55771-6_89
https://doi.org/10.1007/978-3-662-55771-6_89
Autor:
Per Gunnar Kjeldsberg, Robert Schöne, Michael Gerndt, Lubomir Riha, Venkatesh Kannan, Kai Diethelm, Marie-Christine Sawley, Jan Zapletal, Andreas Gocht, Nico Reissmann, Ondrej Vysocky, Madhura Kumaraswamy, Wolfgang E. Nagel
Publikováno v:
System-Scenario-based Design Principles and Applications ISBN: 9783030203429
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cdb0e01c15b1734b9c2de1a2b40e0af4
https://doi.org/10.1007/978-3-030-20343-6_6
https://doi.org/10.1007/978-3-030-20343-6_6