Open AccessA computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators
Author(s) -
P. Veeresha,
Mehmet Yavuz,
Chandrali Baishya
Publication year - 2021
Publication title -
an international journal of optimization and control: theories and applications/e-an international journal of optimization and control: theories and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.287
H-Index - 6
eISSN - 2146-5703
pISSN - 2146-0957
DOI - 10.11121/ijocta.2021.1177
Subject(s) - mathematics , korteweg–de vries equation , homotopy analysis method , laplace transform , uniqueness , fractional calculus , convergence (economics) , homotopy , flow (mathematics) , kernel (algebra) , mathematical analysis , banach space , order (exchange) , nonlinear system , pure mathematics , finance , geometry , physics , quantum mechanics , economics , economic growth
The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he projected method is elegant amalgamations of q-homotopy analysis scheme and Laplace transform. Three fractional operators are hired in the present study to show their essence in generalizing the models associated with power-law distribution, kernel singular, non-local and non-singular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and convergence for the solution is derived with Banach space. The projected scheme springs the series solution rapidly towards convergence and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional order the physical nature have been captured in plots. The achieved consequences illuminates, the hired solution procedure is reliable and highly methodical in investigating the behaviours of the nonlinear models of both integer and fractional order.