What does this research mean for the field?

Unique solutions for inverse problems of the fractional diffusion equation with the Hilfer operator can be established and constructed using Volterra-type integral equations and the Fourier method. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to investigate inverse problems related to the fractional diffusion equation with the Hilfer operator.

May 20, 2026Russian Mathematics

Inverse Problems for the Fractional Diffusion Equation with the Hilfer Operator

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Authors

DDD. K. DurdievAcademy of Sciences Republic of Uzbekistan HTH. H. TurdievAcademy of Sciences Republic of Uzbekistan RRR. R. RashidovBukhara State University

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Implication

Randomized trial explores solutions to inverse problems in fractional diffusion equations, indicating unique methods for coefficient determination.

Key Points

The aim is to investigate inverse problems related to the fractional diffusion equation with the Hilfer operator.
Initial-boundary value problem analyzed for fractional diffusion equation with Cauchy-type initial data.
Time-dependent coefficient identified through a Volterra-type integral equation using contraction mapping principle.
Function determined based on spatial variable studied via Fourier method and Mittag-Leffler function properties.
Existence and uniqueness of the solution for the first inverse problem is proven.
The solution for the second inverse problem is constructed as a series based on eigenfunctions.

Cite This Study

Durdiev et al. (2026) studied this question.

synapsesocial.com/papers/6a0d4e9df03e14405aa99d9e https://doi.org/10.3103/s1066369x26700015

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Implication

Randomized trial explores solutions to inverse problems in fractional diffusion equations, indicating unique methods for coefficient determination.

Inverse Problems for the Fractional Diffusion Equation with the Hilfer Operator

Discussion

Member takes

Implication

Key Points

Cite This Study

Inverse Problems for the Fractional Diffusion Equation with the Hilfer Operator

Discussion

Member takes

Implication

Key Points

Cite This Study

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