Abstract 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.
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Christian Engström
Elmira Nabizadeh Morsalfard
Fractional Calculus and Applied Analysis
Linnaeus University
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Engström et al. (Thu,) studied this question.
www.synapsesocial.com/papers/69a287b00a974eb0d3c03a57 — DOI: https://doi.org/10.1007/s13540-026-00509-6