In the current work, we study a Cauchy problem for time-fractional pseudo-parabolic equation with globally Lipschitz source term. We prove unique existence of mild solution to problem, by common Banach fixed point theorem. This is then verified that exists in time Gr¨onwall’s inequality. Compare previous works about similar issuse, approach way does not require using weighted spaces. Although o...

In this paper, we derive the representation formula of solution for ?-Hilfer fractional differential equation with constant coefficient in form Mittag-Leffler function by using Picard’s successive approximation. Moreover, some properties and fixed point theorems such as Banach Schaefer, introduce new results qualitative existence uniqueness. The generalized Gronwall inequality lemma is used ana...

Trong bài nghiên cứu này, chúng tôi xem xét phương trình được Grotowski đưa ra vào năm 2001 để các nghiệm đặc biệt của dòng nhiệt Yang-Mills trên đa tạp Riemann. Chúng toán Cauchy cho trong không gian . Phương pháp dựa tính chính quy nửa nhóm giải tích Bài tương thích với đã nêu. Bằng cách chuyển đổi thành một thứ 2 và tìm hàm trọng hợp điều khiển đại lượng phi tuyến bị chặn như là khó khăn toá...

The purpose of this study is to propose a high-accuracy and fast numerical method for the Cauchy problem of the Laplace equation. Our problem is directly discretized by the method of fundamental solutions (MFS). The Tikhonov regularization method stabilizes a numerical solution of the problem for given Cauchy data with high noises. The accuracy of the numerical solution depends on a regularizat...

The Cauchy problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodynamically perfect and polytropic. A corresponding initial-boundary value problem has a unique strong solution on ]0, 1[×]0, T [, for each T > 0. By using this result we construct a sequence of approximate solutions which converges to a sol...

Recognizing human facial expression and emotion by computer is an interesting and challenging problem. In this paper we propose a method for recognizing emotions through facial expressions displayed in video sequences. We introduce the Cauchy Naive Bayes classifier which uses the Cauchy distribution as the model distribution and we provide a framework for choosing the best model distribution as...

In this paper we propose a computational method for solving a Cauchy problem of Laplace’s equation. By using the Green formula, the Cauchy problem is transformed to a moment problem so that numerical computations by using a regularization technique can be achieved. Stability estimation and suitable choice of regularization parameter for the proposed method are also given. For numerical verifica...