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Backward Homogeneous Heat Equation with Ψ-Caputo Time Derivative and Spectral Fractional Laplacian
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∈(0,1) with respect to a time scale function Ψ, together with a spectral fractional Laplacian operator of order s∈(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
@misc{ojeda2026backward,
title = {{Backward Homogeneous Heat Equation with $Ψ$-Caputo Time Derivative and Spectral Fractional Laplacian}},
author = {Nelson R. Ojeda and Ruben D. Spies},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28463},
eprint = {2610.28463},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28463},
}
RIS
TY - UNPB
TI - Backward Homogeneous Heat Equation with Ψ-Caputo Time Derivative and Spectral Fractional Laplacian
AU - Nelson R. Ojeda
AU - Ruben D. Spies
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28463
UR - https://arxiv.org/abs/2610.28463
AB - 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∈(0,1) with respect to a time scale function Ψ, together with a spectral fractional Laplacian operator of order s∈(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.
ER -