<p>This article presents an approximate analytical approach for solving the time-fractional Ito equation using the reproducing kernel Hilbert space method. The time-fractional Ito equation provides a more general framework than the standard soliton models. To address this challenging model, a reproducing kernel Hilbert space based framework is introduced, which provide an efficient representation for solving fractional-order differential and integral equations. By employing kernel functions associated with fractional differentiation and integration, the time domain does not need any discretization, making the proposed analytical technique smooth, efficient, and highly effective for simulating the time-fractional Ito equation. The developed numerical scheme exhibits rapid converge and high accuracy in handling fractional time derivatives. Several numerical examples are presented to demonstrate the effectiveness and reliability of the proposed method, highlighting its potential applicability in modeling complex phenomena arising in fields such as physics, finance, and biology.</p>

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Numerical simulation of fifth-order nonlinear complex soliton model in a kernel space

  • Gayatri Das,
  • Ankur Kanaujiya

摘要

This article presents an approximate analytical approach for solving the time-fractional Ito equation using the reproducing kernel Hilbert space method. The time-fractional Ito equation provides a more general framework than the standard soliton models. To address this challenging model, a reproducing kernel Hilbert space based framework is introduced, which provide an efficient representation for solving fractional-order differential and integral equations. By employing kernel functions associated with fractional differentiation and integration, the time domain does not need any discretization, making the proposed analytical technique smooth, efficient, and highly effective for simulating the time-fractional Ito equation. The developed numerical scheme exhibits rapid converge and high accuracy in handling fractional time derivatives. Several numerical examples are presented to demonstrate the effectiveness and reliability of the proposed method, highlighting its potential applicability in modeling complex phenomena arising in fields such as physics, finance, and biology.