On a backward problem for fractional diffusion equation with Riemann‐Liouville derivative
Copyright policy )On a backward problem for fractional diffusion equation with Riemann‐Liouville derivative
In the present paper, we study the initial inverse problem (backward problem) for a two‐dimensional fractional differential equation with Riemann‐Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well‐posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L2 and Hτ norms is considered and illustrated by numerical example.
- An Giang University Viet Nam
- Vietnam National University, Ho Chi Minh City Viet Nam
- Institute of Space Science Romania
- University of Da Nang Viet Nam
- Ton Duc Thang University Viet Nam
random noise, regularized solution, Linear operators and ill-posed problems, regularization, Ill-posed problems for PDEs, PDEs with randomness, stochastic partial differential equations, Nonparametric regression and quantile regression, Initial value problems for second-order parabolic equations, Fractional partial differential equations
random noise, regularized solution, Linear operators and ill-posed problems, regularization, Ill-posed problems for PDEs, PDEs with randomness, stochastic partial differential equations, Nonparametric regression and quantile regression, Initial value problems for second-order parabolic equations, Fractional partial differential equations
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