Existence of solutions to uncertain differential equations of nonlocal type via an extended Krasnosel’skii fixed point theorem

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URI: http://hdl.handle.net/10347/29995
E-ISSN: 2190-5444
DOI: 10.1140/epjp/s13360-022-03447-3

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2022

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Springer
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In the present study, we investigate the existence of the solutions to a type of uncertain differential equations subject to nonlocal derivatives. The approach is based on the application of an extended Krasnosel’skii fixed point theorem valid on fuzzy metric spaces. With this theorem, we deduce that the problem of interest has a fuzzy solution, which is defined on a certain interval. Our approach includes the consideration of a related integral problem, to which the above-mentioned tools are applicable. We finish with some physical motivations

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Khastan, A., Nieto, J.J. & Rodríguez-López, R. Existence of solutions to uncertain differential equations of nonlocal type via an extended Krasnosel’skii fixed point theorem. Eur. Phys. J. Plus 137, 1308 (2022). https://doi.org/10.1140/epjp/s13360-022-03447-3

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We are grateful to the Editor and the anonymous Referees for their comments and suggestions that helped to improve the paper. The research of J.J.N. and R.R.L. is supported by grant numbers PID2020-113275GB-I00 (AEI/FEDER, UE), MTM2016-75140-P (AEI/FEDER, UE), and ED431C 2019/02 (GRC Xunta de Galicia). The visit of A.K. to the University of Santiago de Compostela has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain, co-financed by the European Fund for Regional Development (FEDER) corresponding to the 2014-2020 multiyear financial framework, project MTM2016-75140-P; and by Xunta de Galicia under grant ED431C 2019/02. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature

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© 2022 The Authors. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/
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Estatística, Análise Matemática e Optimización