What does this research mean for the field?

A time-dependent coefficient in a time-fractional diffusion equation with non-strongly regular two-point boundary conditions can be successfully identified by decomposing the solution into symmetric and antisymmetric parts. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Identify an unknown time-dependent coefficient in a time-fractional diffusion equation governed by irregular two-point boundary conditions.

September 10, 2026Mathematical Methods in the Applied Sciences

Identification of the Time‐Dependent Coefficients in the Fractional Diffusion Equation With Two‐Point Boundary Conditions

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Authors

BDBauyrzhan Derbissaly AAArshyn Altybay DSDaurenbek Serikbaev

Discussion

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Overview

Theoretical analysis reveals a method to reconstruct time-dependent parameters in fractional diffusion equations, suggesting a robust framework for handling irregular boundary conditions.

Key Points

Identify an unknown time-dependent coefficient in a time-fractional diffusion equation governed by irregular two-point boundary conditions.
Formulated an inverse problem to recover a time-dependent parameter using an overdetermination condition specified at the midpoint of the spatial interval.
Addressed the failure of the direct Fourier method by decomposing the solution into symmetric and antisymmetric components.
Reduced the original spectral problem into two auxiliary sub-problems to enable mathematical analysis.
Demonstrated that splitting the problem into symmetric and antisymmetric components bypasses irregularities in the two-point boundary conditions.
Established an analytical procedure to uniquely determine the unknown time-dependent coefficient from midpoint measurement data.

Cite This Study

Derbissaly et al. (2026) studied this question.

synapsesocial.com/papers/6aa27b5758559d80afc747d2 https://doi.org/10.1002/mma.70958

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September 10, 2026Mathematical Methods in the Applied Sciences

Identification of the Time‐Dependent Coefficients in the Fractional Diffusion Equation With Two‐Point Boundary Conditions

View Full Paper

Ask AI

Bookmark

Authors

BDBauyrzhan Derbissaly AAArshyn Altybay DSDaurenbek Serikbaev

Discussion

Member takes

Overview

Theoretical analysis reveals a method to reconstruct time-dependent parameters in fractional diffusion equations, suggesting a robust framework for handling irregular boundary conditions.

Key Points

Identify an unknown time-dependent coefficient in a time-fractional diffusion equation governed by irregular two-point boundary conditions.
Formulated an inverse problem to recover a time-dependent parameter using an overdetermination condition specified at the midpoint of the spatial interval.
Addressed the failure of the direct Fourier method by decomposing the solution into symmetric and antisymmetric components.
Reduced the original spectral problem into two auxiliary sub-problems to enable mathematical analysis.
Demonstrated that splitting the problem into symmetric and antisymmetric components bypasses irregularities in the two-point boundary conditions.
Established an analytical procedure to uniquely determine the unknown time-dependent coefficient from midpoint measurement data.

Cite This Study

Derbissaly et al. (2026) studied this question.

synapsesocial.com/papers/6aa27b5758559d80afc747d2 https://doi.org/10.1002/mma.70958

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