On an Initial Value Problem for Nonconvex-Valued Fractional Differential

V. V. Obukhovskii ; G. Petrosyan ; M. Soroka

Matematičeskie zametki, Tome 115 (2024) no. 3, pp. 392-407

Résumé

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.

Détail

Keywords: initial value problem, fractional derivative, differential inclusion, noncompactness measure, integral operator, condensing map.

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