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Backward Subdiffusion
The numerical analysis of inverse problems for subdiffusion is still scarce, due to their inherent ill-posed nature, i.e., the solution does not...
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On a robust stability criterion in the subdiffusion equation with Caputo–Dzherbashian fractional derivative
This paper presents a robust stability criterion for the subdiffusion equation with Caputo–Dzherbashian fractional derivative. The criterion is...
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Optimal Control with Subdiffusion Constraint
So far, we have focused the discussions on the efficient and accurate numerical approximation of the model ( 1.1...
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A robust stability criterion in the one-dimensional subdiffusion equation with Caputo–Fabrizio fractional derivative
In this paper, we present a robust stability criterion for the one-dimensional subdiffusion equation with Caputo–Fabrizio fractional derivative. The...
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Semilinear Subdiffusion
So far, we have only discussed the numerical treatment of linear time-fractional evolution models.
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Numerical Reconstruction of a Discontinuous Diffusive Coefficient in Variable-Order Time-Fractional Subdiffusion
We consider a discontinuous coefficient reconstruction problem associated with a variable-order time-fractional subdiffusion equation. Both interface...
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Inverse Source Problem for the Subdiffusion Equation on a Metric Star Graph with Integral Overdetermination Condition
AbstractIn this article, it is investigated the inverse source problem for the subdiffusion equation on the metric star graph in Sobolev space with...
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A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative
This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In...
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An accurate and efficient space-time Galerkin spectral method for the subdiffusion equation
In this paper, we design and analyze a space-time spectral method for the subdiffusion equation. Here, we are facing two difficulties. The first is...
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A Corrected L1 Method for a Time-Fractional Subdiffusion Equation
Piecewise linear interpolation has been widely applied to discretize the Caputo fractional derivative operator that yields the widely used L1 method....
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Discovery of Subdiffusion Problem with Noisy Data via Deep Learning
Data-driven discovery of partial differential equations (PDEs) from observed data in machine learning has been developed by embedding the discovery...
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Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations
We consider new numerical schemes to solve two different systems of nonlinear fractional reaction subdiffusion equations. These systems of equations...
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Approximation of the Subdiffusion Equation with Solution-dependent Fractional Time Derivative and Diffusion Coefficient
AbstractWe consider a boundary value problem for a nonlinear subdiffusion equation with Caputo fractional time derivative of the order
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Long and Short Time Behavior of Non-local in Time Subdiffusion Equations
This paper is devoted to studying the long and short time behavior of the solutions to a class of non-local in time subdiffusion equations. To this...
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A time-fractional superdiffusion wave-like equation with subdiffusion possibly dam** term: well-posedness and Mittag-Leffler stability
In this article, we focus on the application of the recent notion of time-fractional derivative developed in Sobolev spaces to the study of...
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Cauchy Problem for Subdiffusion Equation on Metric Star Graph with Edge Dependent Order of Time-Fractional Derivative
AbstractThis work is devoted to study the Cauchy problem for subdiffusion equation on the metric star graph with edge-dependent order of...
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A Novel Spectral Method for the Subdiffusion Equation
In this paper, we design and analyze a novel spectral method for the subdiffusion equation. As it has been known, the solutions of this equation are...
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Convergence Rates of a Finite Difference Method for the Fractional Subdiffusion Equations
We consider the convergence of an effective numerical method of the subdiffusion equation with the Caputo fractional derivative in time. We...
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Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise
We investigate a semilinear stochastic time-space fractional subdiffusion equation driven by fractionally integrated multiplicative noise. The...