Well-Posedness for Time-Fractional Diffusion With Singular Multiplicative Forcing

Ngo Ngoc Hung

Journal of Applied Mathematics, 2026, vol. 2026, 1-11

Abstract: We consider a time-fractional diffusion equation on ℠with a possibly singular multiplicative forcing term. By exploiting an operator convolution identity, the original mild formulation is reduced to a Volterra integral equation involving the fractional diffusion family. Using standard Mittag–Leffler kernel estimates, scaling-consistent Lp℠–Lq℠smoothing bounds, and time-weighted convolution estimates, we establish existence and uniqueness of mild solutions in suitable time-weighted spaces. The forcing profile is allowed to be nonsmooth in space and to exhibit an integrable singularity near t=0, whereas the nonlinearity is assumed to be globally Lipschitz with σ0=0. We further prove that the solution attains the prescribed initial data in Lq℠and depends continuously on both the initial data and the multiplicative forcing profile.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:2216739

DOI: 10.1155/jama/2216739

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