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Creators/Authors contains: "Zheng, Xiangcheng"

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  1. ; ; (, SIAM Journal on Applied Mathematics)
    Free, publicly-accessible full text available April 30, 2026
  2. ; ; (, Fractional Calculus and Applied Analysis)
    Abstract In this article, using that the fractional Laplacian can be factored into a product of the divergence operator, a Riesz potential operator and the gradient operator, we introduce an anomalous fractional diffusion operator, involving a matrixK(x), suitable when anomalous diffusion is being studied in a non homogeneous medium. For the case ofK(x) a constant, symmetric positive definite matrix we show that the fractional Poisson equation is well posed, and determine the regularity of the solution in terms of the regularity of the right hand side function. 
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  3. ; ; ; (, Journal of Integral Equations and Applications)
    Free, publicly-accessible full text available December 1, 2025
  4. ; ; ; (, Numerical Methods for Partial Differential Equations)
    Abstract Fractional diffusion equations exhibit competitive capabilities in modeling many challenging phenomena such as the anomalously diffusive transport and memory effects. We prove the well‐posedness and regularity of an optimal control of a variably distributed‐order fractional diffusion equation with pointwise constraints, where the distributed‐order operator accounts for, for example, the effect of uncertainties. We accordingly develop and analyze a fully‐discretized finite element approximation to the optimal control without any artificial regularity assumption of the true solution. Numerical experiments are also performed to substantiate the theoretical findings. 
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    Free, publicly-accessible full text available November 1, 2025
  5. ; ; (, Multiscale Modeling & Simulation)
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  6. ; ; ; (, SIAM Journal on Scientific Computing)
    Full Text Available 
  7. ; ; ; ; (, Fractal and Fractional)
    We establish both the uniqueness and the existence of the solutions to a hidden-memory variable-order fractional stochastic partial differential equation, which models, e.g., the stochastic motion of a Brownian particle within a viscous liquid medium varied with fractal dimensions. We also investigate the inverse problem concerning the observations of the solutions, which eliminates the analytic assumptions on the variable orders in the literature of this topic and theoretically guarantees the reliability of the determination and experimental inference. 
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  8. ; ; (, Fractional Calculus and Applied Analysis)
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  9. ; ; (, Numerical Algorithms)
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  10. ; ; (, Journal of Computational and Applied Mathematics)
    Full Text Available