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The use of partition polynomial series in Laplace inversion of composite functions with applications in fractional calculus
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
2019 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 42, no 7, p. 2169-2189Article in journal (Refereed) Published
Abstract [en]

This paper presents an analytical method towards Laplace transform inversion of composite functions with the aid of Bell polynomial series. The presented results are used to derive the exact solution of fractional distributed order relaxation processes as well as time-domain impulse response of fractional distributed order operators in new series forms. Evaluation of the obtained series expansions through computer simulations is also given. The results are then used to present novel series expansions for some special functions, including the one-parameter Mittag-Leffler function. It is shown that truncating these series expansions when combined with using potential partition polynomials provides efficient approximations for these functions. At the end, the results are shown to be also useful in studying asymptotical behavior of partial Bell polynomials. Numerical simulations as well as analytical examples are provided to verify the results of this paper.

Place, publisher, year, edition, pages
Wiley , 2019. Vol. 42, no 7, p. 2169-2189
Keywords [en]
anomalous relaxation, Bell polynomial, fractional differential equations, Laplace transform, Mittag Leffler function
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-249767DOI: 10.1002/mma.5472ISI: 000463164900002Scopus ID: 2-s2.0-85062323839OAI: oai:DiVA.org:kth-249767DiVA, id: diva2:1307662
Note

QC 20190429

Available from: 2019-04-29 Created: 2019-04-29 Last updated: 2019-11-07Bibliographically approved

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