Title: Numerical approximation of generalised time - fractional KdV equation on bounded domain

Authors: Kamlesh Kumar; Awadhesh K. Pandey

Addresses: Department of Sciences (Mathematics), Manav Rachna University, Faridabad, HR, India ' Jindal School of Banking and Finance, O.P. Jindal Global University, Sonipat, India

Abstract: We discuss a finite difference scheme (FDS) for the model of Korteweg-de Vries (KdV) equation with new generalised temporal fractional derivative over bounded domain. The generalised fractional derivative (GFD) containing scale and weight functions essentially redefines new derivative for a broader class of functions. Theoretical study shows that the fractional KdV model defined on bounded domain processes dissipative property when Dirichlet boundary condition is employed. The stability and convergence of FDS are also established. Validation of theoretical analysis is shown by two numerical simulations. The numerical findings are shown via tables and figures. The effect of scale function which is appears in GFD is also presented.

Keywords: generalised fractional derivative; GFD; finite difference scheme; FDS; KdV equation.

DOI: 10.1504/IJANS.2025.151205

International Journal of Applied Nonlinear Science, 2025 Vol.5 No.2, pp.180 - 194

Received: 30 Sep 2024
Accepted: 22 Nov 2024
Published online: 19 Jan 2026 *

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