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<p>The issues of the existence and uniqueness of a&#xa0;mild solution for the Cauchy problem to quasilinear equations in Banach spaces with the Gerasimov-Caputo fractional derivatives. It is supposed that the equation contains a&#xa0;linear operator with a&#xa0;non-trivial kernel at the highest-order derivative. A&#xa0;pair of linear operators in the linear part of the equation is assumed to be sectorial. The properties of such a&#xa0;pair make it possible to reduce a&#xa0;degenerate equation to a&#xa0;system of simpler equations on two subspaces. Under some additional restrictions on the nonlinear operator theorems on the existence of a&#xa0;unique mild solution are proved. Abstract results are applied to initial boundary value problems for some systems of partial differential equations.</p>

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Mild solutions of degenerate quasilinear equations with Gerasimov-Caputo derivatives

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Tatyana A. Zakharova

摘要

The issues of the existence and uniqueness of a mild solution for the Cauchy problem to quasilinear equations in Banach spaces with the Gerasimov-Caputo fractional derivatives. It is supposed that the equation contains a linear operator with a non-trivial kernel at the highest-order derivative. A pair of linear operators in the linear part of the equation is assumed to be sectorial. The properties of such a pair make it possible to reduce a degenerate equation to a system of simpler equations on two subspaces. Under some additional restrictions on the nonlinear operator theorems on the existence of a unique mild solution are proved. Abstract results are applied to initial boundary value problems for some systems of partial differential equations.