Existence of solutions to uncertain differential equations of nonlocal type via an extended Krasnosel’skii fixed point theorem
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), 45137-66731, Zanjan, Iran
2 CITMAga, and Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
Accepted: 31 October 2022
Published online: 5 December 2022
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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