Browsing by Author "Ho Duy Binh"

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Citation - WoS: 27
Citation - Scopus: 29
Fractional Order Continuity of a Time Semi-Linear Fractional Diffusion-Wave System
(Elsevier, 2020) Luu Vu Cam Hoan; Karapinar, Erdal; Singh, Jagdev; Ho Duy Binh; Nguyen Huu Can; Nguyen Duc Phuong; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, we consider the time-fractional diffusion equations depend on fractional orders. In more detail, we study on the initial value problems for the time semi-linear fractional diffusion-wave system and discussion about continuity with respect to the fractional derivative order. We find the answer to the question: When the fractional orders get closer, are the corresponding solutions close? To answer this question, we present some depth theories on PDEs and fractional calculus. In addition, we add an example numerical to verify the proposed theory. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
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.
Citation - WoS: 66
Citation - Scopus: 64
On Continuity of the Fractional Derivative of the Time-Fractional Semilinear Pseudo-Parabolic Systems
(Springer, 2021) Ho Duy Binh; Nguyen Hoang Luc; Nguyen Huu Can; Karapinar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order. Moreover, we present an example to illustrate the theory.