Russian Mathematics

, Volume 63, Issue 9, pp 1–11 | Cite as

On the Boundary Value Problem for Functional Differential Inclusion of Fractional Order with General Initial Condition in a Banach Space

  • M. S. AfanasovaEmail author
  • G. G. PetrosyanEmail author


We consider the problem for a functional differential inclusion of fractional order with a general initial condition expressed in the form of an operator inclusion in a Banach space. At the beginning of the paper, an introduction is presented in which the relevance of the study is substantiated, then preliminary information from fractional analysis, the theory of measures of noncompactness and condensing mappings, as well as some information from multivalued analysis are given. In the second subsection, we state the problem and its solution on the basis of the theory of condensing multivalued mappings. In the last subsection, we give an example of a particular case of the solved problem, in the case of an antiperiodic boundary condition.

Key words

differential inclusion fractional derivative measure of noncompactness fixed point condensing multimapping 


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The work of the second author was supported by Ministry of Education and Science of Russian Federation in the framework of project part of state quotum, project no. 1.3464.2017/4.6, and by Russian foundation for Basic Research in the framework of projects no. 19-31-60011 and no. 17-51-52022 MKhT_a.

The work of the first author was supported by Ministry of Education and Science of Russian Federation, project 14.Z50.31.0037.


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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Voronezh State UniversityVoronezhRussia
  2. 2.Voronezh State University of Engineering TechnologiesVoronezhRussia
  3. 3.Voronezh State Pedagogical UniversityVoronezhRussia

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