Work

Backward Homogeneous Heat Equation with $Ψ$-Caputo Time Derivative and Spectral Fractional Laplacian

Year: 2026

Type: preprint

Abstract: In this work, we study a fractional diffusion model in time and space, formulated in an open and bounded domain, involving a Caputo fractional derivative of order $μ\in(0,1)$ with respect to a time scale function $Ψ$, together with a spectral fractional Laplacian operator of order $s\in(0,1)$. The associated direct problem is analyzed, as well as the inverse problem of temporal reconstruction from final data, which is inherently ill-posed. Through a spectral representation, the instability of the problem and the effect of the choice of the function $Ψ$ on the amplification of spectral modes are examined.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28463

Authors: Ojeda, Nelson R., Spies, Ruben D.

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional del Litoral, National University of Formosa

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223099233

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