A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo–Fabrizio time-fractional derivative
The present article aims to present a comprehensive study on a nonlinear time-fractional model involving the Caputo–Fabrizio (CF) derivative. More explicitly, a new ( 2 + 1 ) -dimensional mKdV (2D-mKdV) equation involving the Caputo–Fabrizio time-fractional derivative is considered and an analytic a...
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Published in | Advances in difference equations Vol. 2020; no. 1; pp. 1 - 13 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
06.07.2020
Springer Nature B.V SpringerOpen |
Subjects | |
Online Access | Get full text |
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Summary: | The present article aims to present a comprehensive study on a nonlinear time-fractional model involving the Caputo–Fabrizio (CF) derivative. More explicitly, a new
(
2
+
1
)
-dimensional mKdV (2D-mKdV) equation involving the Caputo–Fabrizio time-fractional derivative is considered and an analytic approximation for it is retrieved through a systematic technique, called the homotopy analysis transform (HAT) method. Furthermore, after proving the Lipschitz condition for the kernel
ψ
(
x
,
y
,
t
;
u
)
, the fixed-point theorem is formally utilized to demonstrate the existence and uniqueness of the solution of the new 2D-mKdV equation involving the CF time-fractional derivative. A detailed study finally is carried out to examine the effect of the Caputo–Fabrizio operator on the dynamics of the obtained analytic approximation. |
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ISSN: | 1687-1847 1687-1839 1687-1847 |
DOI: | 10.1186/s13662-020-02789-5 |