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<p>In this paper, we consider a boundary value problem for Hale type differential inclusions of fractional order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \in (1,2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> in a separable Banach space under the assumption that the linear part of the inclusion is a generator of a uniformly bounded strongly continuous family of cosine operator functions and the nonlinear part is a causal multivalued operator. Based on the fixed point theory for condensing maps, we establish the global existence of a mild solution to this problem.</p>

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BOUNDARY VALUE PROBLEM OF HALE TYPE DIFFERENTIAL INCLUSIONS OF FRACTIONAL ORDER WITH CAUSAL MULTIOPERATOR IN BANACH SPACE

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Garik Petrosyan,
  • Maria Soroka

摘要

In this paper, we consider a boundary value problem for Hale type differential inclusions of fractional order \(\alpha \in (1,2)\) α ∈ ( 1 , 2 ) in a separable Banach space under the assumption that the linear part of the inclusion is a generator of a uniformly bounded strongly continuous family of cosine operator functions and the nonlinear part is a causal multivalued operator. Based on the fixed point theory for condensing maps, we establish the global existence of a mild solution to this problem.