# Generalized uniformly continuous solution operators and inhomogeneous fractional evolution equations with variable coefficients

 dc.contributor.author Japundzic, Milos dc.contributor.author Rajter-Ciric, Danijela dc.date.accessioned 2022-09-26T17:52:39Z dc.date.available 2022-09-26T17:52:39Z dc.date.issued 2017-11-27 dc.description.abstract We consider Cauchy problem for inhomogeneous fractional evolution equations with Caputo fractional derivatives of order 0 < α < 1 and variable coefficients depending on x. In order to solve this problem we introduce generalized uniformly continuous solution operators and use them to obtain the unique solution on a certain Colombeau space. In our solving procedure, instead of the original problem we solve a certain approximate problem, but therefore we also prove that the solutions of these two problems are associated. At the end, we illustrate the applications of the developed theory by giving some appropriate examples. dc.description.department Mathematics dc.format Text dc.format.extent 24 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Japundzic, M., & Rajter-Ciric, D. (2017). Generalized uniformly continuous solution operators and inhomogeneous fractional evolution equations with variable coefficients. Electronic Journal of Differential Equations, 2017(293), pp. 1-24. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/16165 dc.language.iso en dc.publisher Texas State University, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. dc.subject Fractional evolution equation dc.subject Fractional Duhamel principle dc.subject Generalized Colombeau solution operator dc.subject Fractional derivative dc.subject Mittag-Leffler type function dc.title Generalized uniformly continuous solution operators and inhomogeneous fractional evolution equations with variable coefficients dc.type Article

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