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Browsing by Author "Anh Tuan Nguyen"

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    Citation - WoS: 4
    Citation - Scopus: 4
    On a Fractional Parabolic Equation With Regularized Hyper-Bessel Operator and Exponential Nonlinearities
    (Mdpi, 2022) Ho Duy Binh; Anh Tuan Nguyen; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. More specifically, we examine the existence and uniqueness of mild solutions in Hilbert scale-spaces which are constructed by a uniformly elliptic symmetry operator on a smooth bounded domain. Our main argument is based on the Banach principle argument. In order to achieve the necessary and sufficient requirements of this argument, we have smoothly combined the application of the Fourier series supportively represented by Mittag-Leffler functions, with Hilbert spaces and Sobolev embeddings. Because of the presence of the fractional operator, we face many challenges in handling proper integrals which appear in the representation of mild solutions. Besides, the source term of an exponential type also causes trouble for us when deriving the desired results. Therefore, powerful embeddings are used to limit the growth of nonlinearity.
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    Citation - WoS: 10
    Citation - Scopus: 12
    Regularization of the Inverse Problem for Time Fractional Pseudo-Parabolic Equation With Non-Local in Time Conditions
    (Springer Heidelberg, 2022) Le Dinh Long; Anh Tuan Nguyen; Baleanu, Dumitru; Nguyen Duc Phuong; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    This paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the problem is non-well posed and the stability of the source function. Second, by using the Modified Fractional Landweber method, we present regularization solutions and show the convergence rate between regularization solutions and sought solution are given under a priori and a posteriori choice rules of the regularization parameter, respectively. Finally, we present an illustrative numerical example to test the results of our theory.