Three regularization methods for identifying the initial value of time fractional advection–dispersion equation

Yang, Fan; Wu, Hang-Hang; Li, Xiaoxiao

doi:10.1007/s40314-022-01762-0

Cited by 7 publications

(2 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Lemma 4. [24] Assume that 0 < α 0 < α 1 < 1. Then, there exist constants D ± > 0, depending only on α 0 , α 1 such that for all α ∈ [α 0 , α 1 ], we obtain…”

Section: Preliminarymentioning

confidence: 99%

See 1 more Smart Citation

Simultaneous Inversion of the Source Term and Initial Value of the Time Fractional Diffusion Equation

Yang,

Xu,

2024

Mathematical Modelling and Analysis

Self Cite

View full text Add to dashboard Cite

In this paper, the problem we investigate is to simultaneously identify the source term and initial value of the time fractional diffusion equation. This problem is ill-posed, i.e., the solution (if exists) does not depend on the measurable data. We give the conditional stability result under the a-priori bound assumption for the exact solution. The modified Tikhonov regularization method is used to solve this problem, and under the a-priori and the a-posteriori selection rule for the regularization parameter, the convergence error estimations for this method are obtained. Finally, numerical example is given to prove the effectiveness of this regularization method.

show abstract

“…Lemma 4. [24] Assume that 0 < α 0 < α 1 < 1. Then, there exist constants D ± > 0, depending only on α 0 , α 1 such that for all α ∈ [α 0 , α 1 ], we obtain…”

Section: Preliminarymentioning

confidence: 99%

“…At this time, we obtain the iterative format by discretizing the equation, and then obtain g, f from the iterative format. Using the discrete format of the Caputo derivative in [24], the following iterative scheme is obtained…”

Section: Numerical Experimentsmentioning

confidence: 99%

Simultaneous Inversion of the Source Term and Initial Value of the Time Fractional Diffusion Equation

Yang,

Xu,

2024

Mathematical Modelling and Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

Logarithmic convexity of non‐symmetric time‐fractional diffusion equations

Chorfi,

Maniar,

Yamamoto

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

We consider a class of diffusion equations with the Caputo time‐fractional derivative subject to the homogeneous Dirichlet boundary conditions. Here, we consider a fractional order and a second‐order operator which is elliptic and non‐symmetric. In this paper, we show that the logarithmic convexity extends to this non‐symmetric case provided that the drift coefficient is given by a gradient vector field. Next, we perform some numerical experiments to validate the theoretical results in both symmetric and non‐symmetric cases. Finally, some conclusions and open problems will be mentioned.

show abstract

Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator

Yang,

Cao,

2024

Fract Calc Appl Anal

View full text Add to dashboard Cite

Three regularization methods for identifying the initial value of time fractional advection–dispersion equation

Cited by 7 publications

References 39 publications

Simultaneous Inversion of the Source Term and Initial Value of the Time Fractional Diffusion Equation

Simultaneous Inversion of the Source Term and Initial Value of the Time Fractional Diffusion Equation

Logarithmic convexity of non‐symmetric time‐fractional diffusion equations

Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator

Contact Info

Product

Resources

About