A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

Pundikala Veeresha; Mehmet Yavuz; Chandrali  Baishya

doi:10.11121/ijocta.2021.1177

Authors

Pundikala Veeresha Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, India https://orcid.org/0000-0002-4468-3048
Mehmet Yavuz Necmettin Erbakan University, Faculty of Science, Department of Mathematics and Computer Sciences, 42090, Konya, Turkey https://orcid.org/0000-0002-3966-6518
Chandrali Baishya Department of Studies and Research in Mathematics, Tumkur University, Tumkur-572103, India https://orcid.org/0000-0002-9653-313X

DOI:

https://doi.org/10.11121/ijocta.2021.1177

Keywords:

Force KdV equation, Fractional derivatives, q-Homotopy analysis transform technique, Fixed point theorem

Abstract

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.

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Author Biographies

Pundikala Veeresha, Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, India

is an Assistant Professor in the Department of Mathematics, CHRIST (Deemed to be University), Bengaluru. He completed his Master's Degree from Davangere University, Davangere, and his Ph.D. from Karnatak University, Dharwad. His areas of research interest includes Fractional Calculus, Mathematical Modelling, Numerical and Analytical Methods, and Mathematical Physics. He has been the author of more than 70 research articles published in highly reputed journals.

Mehmet Yavuz, Necmettin Erbakan University, Faculty of Science, Department of Mathematics and Computer Sciences, 42090, Konya, Turkey

received his Ph.D. in Mathematics from Balıkesir University, Turkey. He visited the University of Exeter, U.K. for post-doctoral research in mathematical biology and optimal control theory for a year. He is currently serving as an associate professor at Necmettin Erbakan University, Turkey. His research interests mainly focus on infectious disease dynamics, fractional mathematical modeling, fractional theory and method, optimal control theory and bifurcation analysis. He has published more than 60 research papers in international esteemed journals and he is a reviewer for about seventy international repute journals as well as he is Editor-in-Chief of the "Mathematical Modelling and Numerical Simulation with Applications" journal.

Chandrali Baishya, Department of Studies and Research in Mathematics, Tumkur University, Tumkur-572103, India

has obtained her PhD degree in Mathematical Sciences from the University of Mysore, Karnataka, India in 2009. She has been working as Assistant Professor in Tumkur University, Karnataka, India since 2011. Her areas of research interest are numerical analysis, fractional differential equations and mathematical biology.

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