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<p>In this work, we investigate the well-posedness and regularity of solutions to an abstract fractional differential equation that incorporates additional memory effects arising from nonlocal-in-time operators. Such equations are of interest because of their relevance in modeling complex phenomena, such as anomalous diffusion and viscoelastic behavior. We reformulate the problem as a perturbation of a parabolic Volterra integral equation. By applying Laplace transform techniques and resolvent estimates, we establish existence, uniqueness, and regularity results under mild assumptions on the underlying operators and memory kernels.</p>

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On multiterm time-fractional diffusion equations with additional memory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月26日

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  • Christian Engström,
  • Elmira Nabizadeh Morsalfard

摘要

In this work, we investigate the well-posedness and regularity of solutions to an abstract fractional differential equation that incorporates additional memory effects arising from nonlocal-in-time operators. Such equations are of interest because of their relevance in modeling complex phenomena, such as anomalous diffusion and viscoelastic behavior. We reformulate the problem as a perturbation of a parabolic Volterra integral equation. By applying Laplace transform techniques and resolvent estimates, we establish existence, uniqueness, and regularity results under mild assumptions on the underlying operators and memory kernels.