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On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator
On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator
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Date
2023
Authors
Bui Dai Nghia, Van Tien Nguyen, and Le Dinh Long
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Abstract
"In this article, we considered the pseudo-parabolic equation with Caputo-Fabrizio fractional
derivative. This equation has many applications in different fields, such as science, technology, and so
on. In this article, we gave the formula of mild solution, which is represented in the form of Fourier series by
some operators . In the linear case, we investigated the continuity of the mild solution with respect to the
fractional order. For the nonlinear case, we investigated the existence and uniqueness of a global solution.
The main proof technique is based on the Banach fixed point theorem combined with some Sobolev
embeddings. For more detailed, we obtained two other interesting results: the continuity of mild solution
with respect to the derivative order and the convergence of solution as the coefficient k approaches to zero."
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Keywords
"Caputo-Fabrizio derivative operator,
Burger equation,
Banach fixed point theory,
Sobolev embeddings"