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NEW RESULTS FOR PARABOLIC EQUATION ON THE SPHERE WITH CAPUTO–FABRIZIO OPERATOR
NEW RESULTS FOR PARABOLIC EQUATION ON THE SPHERE WITH CAPUTO–FABRIZIO OPERATOR
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Date
2022
Authors
NGUYEN ANH TUAN
NGUYEN HOANG LUC
NGUYEN PHAM QUYNH TRANG
HO THI KIM VAN
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Abstract
In this paper, we are interested in studying the initial value problem for parabolic problem associated with the Caputo–Fabrizio derivative. We deal the problem in two cases: linear inhomogeneous case and nonlinearity source term. For the linear case, we derive the convergence result of the mild solution when the fractional order [Formula: see text] under some various assumptions on the initial datum. For the nonlinear problem, we show the existence and uniqueness of the mild solution using Banach fixed point theory. We also prove the convergence result of the mild solution when the fractional order [Formula: see text].
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Keywords
Nonlocal Parabolic Equation,
Banach Fixed Point Theory,
SphereRegularity,
Caputo–Fabrizio Operator,
Convergence