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

Nelson R. Ojeda; Ruben D. Spies

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arXiv · 2610.28463

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

Nelson R. Ojeda·Ruben D. Spies

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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.

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BibTeX RIS

Nelson R. Ojeda, Ruben D. Spies. 2026-10-20. Backward Homogeneous Heat Equation with $Ψ$-Caputo Time Derivative and Spectral Fractional Laplacian. https://arxiv.org/abs/2610.28463

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