Journal Articles - Mathematic and Statistic - 2022

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Inverse Source Problem for Sobolev Equation with Fractional Laplacian

( 2022)
Nguyen Duc Phuong
;
Van Tien Nguyen
;
Le Dinh Long
;
Yusuf Gurefe

In this paper, we are interested in the problem of determining the source function for the Sobolev equation with fractional Laplacian. This problem is ill-posed in the sense of Hadamard. In order to edit the instability instability of the solution, we applied the fractional Landweber method. In the theoretical analysis results, we show the error estimate between the exact solution and the regularized solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Finally, we investigate the convergence of the source function when fractional order .
Stability of fractional order of time nonlinear fractional diffusion equation with Riemann–Liouville derivative

( 2022)
Le Dinh Long
;
Ho Duy Binh
;
Devendra Kumar
;
Nguyen Hoang Luc
;
Nguyen Huu Can

In this paper, we investigate an equation of nonlinear fractional diffusion with the derivative of Riemann–Liouville. Firstly, we determine the global existence and uniqueness of the mild solution. Next, under some assumptions on the input data, we discuss continuity with regard to the fractional derivative order for the time. Our key idea is to combine the theories Mittag–Leffler functions and Banach fixed-point theorem. Finally, we present some examples to test the proposed theory.