Nonlinear analysis of a nonlinear modified KdV equation under Atangana Baleanu Caputo derivative
[ X ]
Tarih
2022
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Inst Mathematical Sciences-Aims
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The focus of the current manuscript is to provide a theoretical and computational analysis of the new nonlinear time-fractional (2+1)-dimensional modified KdV equation involving the Atangana-Baleanu Caputo (ABC) derivative. A systematic and convergent technique known as the Laplace Adomian decomposition method (LADM) is applied to extract a semi-analytical solution for the considered equation. The notion of fixed point theory is used for the derivation of the results related to the existence of at least one and unique solution of the mKdV equation involving under ABC-derivative. The theorems of fixed point theory are also used to derive results regarding to the convergence and Picard's X-stability of the proposed computational method. A proper investigation is conducted through graphical representation of the achieved solution to determine that the ABC operator produces better dynamics of the obtained analytic soliton solution. Finally, 2D and 3D graphs are used to compare the exact solution and approximate solution. Also, a comparison between the exact solution, solution under Caputo-Fabrizio, and solution under the ABC operator of the proposed equation is provided through graphs, which reflect that ABC-operator produces better dynamics of the proposed equation than the Caputo-Fabrizio one.
Açıklama
Anahtar Kelimeler
Atangana-Baleanu fractional operator, fixed point theory, Laplace Adomian decomposition
Kaynak
Aims Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
7
Sayı
5
