Abstract:
Based on fixed point theory for condensing operators, an initial value problem for semilinear differential inclusions of fractional order $q\in(1,2)$ in Banach spaces is studied. It is assumed that the linear part of the inclusion generates a family of cosine operator functions, and the nonlinear part is a multivalued map with nonconvex values. Local and global existence theorems for integral solutions of the initial value problem are proved.
Keywords:initial value problem, fractional derivative, differential inclusion, noncompactness measure, integral operator, condensing map.
The results of Secs. 3 and 4 were obtained under the financial support
of the Program if the President of the Russian Federation for the State Support
of Young Russian Scientists —Candidates of Science,
under grant MK-338.2021.1.1.
The results of Secs. 5 and 6 were obtained under the financial support
of the Russian Science Foundation, grant no. 22-71-10008,
https://rscf.ru/en/project/22-71-10008/.
Citation:
V. V. Obukhovskii, G. Petrosyan, M. Soroka, “On an Initial Value Problem for Nonconvex-Valued Fractional Differential
Inclusions in a Banach Space”, Mat. Zametki, 115:3 (2024), 392–407; Math. Notes, 115:3 (2024), 358–370
Citation in format AMSBIB
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