On an Initial Value Problem for Nonconvex-Valued Fractional Differential Inclusions in a Banach Space

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030088

V. V. Obukhovskii, G. G. Petrosyan, M. S. Soroka

引用次数: 0

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 mild solutions of the initial value problem are proved.

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论巴拿赫空间中非凸值分式微分夹杂的初值问题

摘要基于凝聚算子的定点理论，研究了巴拿赫空间中分数阶（q\in(1,2)\）半线性微分夹杂的初值问题。假设夹杂的线性部分产生一个余弦算子函数族，而非线性部分是一个具有非凸值的多值映射。证明了初值问题温和解的局部和全局存在定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.