Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 17Citation - Scopus: 18On a Nonlocal Problem for a Caputo Time-Fractional Pseudoparabolic Equation(Wiley, 2021) Hammouch, Zakia; Karapinar, Erdal; Tuan, Nguyen Huy; Nguyen, Anh TuanIn this paper, we consider a class of pseudoparabolic equations with the nonlocal condition and the Caputo derivative. Two cases of problems (1-2) will be studied, which are linear case and nonlinear case. For the first case, we establish the existence, the uniqueness, and some regularity results by using some estimates technique and Sobolev embeddings. Second, the Banach fixed-point theorem will be applied to the nonlinear case to prove the existence and the uniqueness of the mild solution.Article Citation - WoS: 32Citation - Scopus: 30Analysis of the Fractional Corona Virus Pandemic Via Deterministic Modeling(Wiley, 2021) Tri, Vo Viet; Baleanu, Dumitru; Tuan, Nguyen HuyWith every passing day, one comes to know that cases of the corona virus disease are increasing. This is an alarming situation in many countries of the globe. So far, the virus has attacked as many as 188 countries of the world and 5 549 131 (27 May 2020) human population is affected with 348 224 deaths. In this regard, public and private health authorities are looking for manpower with modeling skills and possible vaccine. In this research paper, keeping in view the fast transmission dynamics of the virus, we have proposed a new mathematical model of eight mutually distinct compartments with the help of memory-possessing operator of Caputo type. The fractional order parameter psi of the model has been optimized so that smallest error can be attained while comparing simulations and the real data set which is considered for the country Pakistan. Using Banach fixed point analysis, it has been shown that the model has a unique solution whereas its basic reproduction numberR0is approximated to be 6.5894. Disease-free steady state is shown to be locally asymptotically stable forR0<0, otherwise unstable. Nelder-Mead optimization algorithm under MATLAB Toolbox with daily real cases of the virus in Pakistan is employed to obtain best fitted values of the parameters for the model's validation. Numerical simulations of the model have come into good agreement with the practical observations wherein social distancing, wearing masks, and staying home have proved to be the most effective measures in order to prevent the virus from further spread.Article Citation - WoS: 16Citation - Scopus: 17On a Backward Problem for Fractional Diffusion Equation With Riemann-Liouville Derivative(Wiley, 2020) Nguyen Hoang Tuan; Baleanu, Dumitru; Tran Ngoc Thach; Nguyen Huy Tuan; Thach, Tran Ngoc; Tuan, Nguyen HuyIn 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 L-2 and H-tau norms is considered and illustrated by numerical example.Article Citation - WoS: 20Regularization of a Terminal Value Problem for Time Fractional Diffusion Equation(Wiley, 2020) Vo Van Au; Le Dinh Long; Baleanu, Dumitru; Nguyen Huy Tuan; Nguyen Anh Triet; Au, Vo Van; Long, Le Dinh; Tuan, Nguyen Huy; Triet, Nguyen AnhIn this article, we study an inverse problem with inhomogeneous source to determine an initial data from the time fractional diffusion equation. In general, this problem is ill-posed in the sense of Hadamard, so the quasi-boundary value method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules and analyze them. Finally, two numerical results in the one-dimensional and two-dimensional case show the evidence of the used regularization method.Article Citation - WoS: 31Citation - Scopus: 34On a Terminal Value Problem for a Generalization of the Fractional Diffusion Equation With Hyper-Bessel Operator(Wiley, 2020) Le Nhat Huynh; Baleanu, Dumitru; Nguyen Huu Can; Nguyen Huy Tuan; Huynh, Le Nhat; Tuan, Nguyen Huy; Can, Nguyen HuuIn this paper, we consider an inverse problem of recovering the initial value for a generalization of time-fractional diffusion equation, where the time derivative is replaced by a regularized hyper-Bessel operator. First, we investigate the existence and regularity of our terminal value problem. Then we show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Tikhonov regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.Article Regularized Solution for Nonlinear Elliptic Equations With Random Discrete Data(Wiley, 2019) Nguyen Huy Tuan; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Duc Phuong; Duc Phuong, Nguyen; Hoang Luc, Nguyen; Phuong, Nguyen Duc; Tuan, Nguyen Huy; Luc, Nguyen HoangThe aim of this paper is to study the Cauchy problem of determining a solution of nonlinear elliptic equations with random discrete data. A study showing that this problem is severely ill posed in the sense of Hadamard, ie, the solution does not depend continuously on the initial data. It is therefore necessary to regularize the in-stable solution of the problem. First, we use the trigonometric of nonparametric regression associated with the truncation method in order to offer the regularized solution. Then, under some presumption on the true solution, we give errors estimates and convergence rate in L-2-norm. A numerical example is also constructed to illustrate the main results.