Computational analysis of fractional Drinfeld-Sokolov-Wilson equation associated with regularized form of Hilfer-Prabhakar derivative

Jagdev Singh; Arpita Gupta; Juan J. Nieto; Moisés Rutkoski; Jagdev Singh; Arpita Gupta; Juan J. Nieto; Moisés Rutkoski

doi:10.3934/nhm.2026001

Networks and Heterogeneous Media

2026, Volume 21, Issue 1: 1-21. doi: 10.3934/nhm.2026001

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Research article

Computational analysis of fractional Drinfeld-Sokolov-Wilson equation associated with regularized form of Hilfer-Prabhakar derivative

1.
Department of Mathematics, JECRC University, Jaipur, Rajasthan
2.
CITMAga (Galician Centre for Mathematical Research and Technology) and Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
3.
CMAT, University of Trás-os-Montes e Alto Douro, 5000-801 Vila Real, Portugal

Received: 29 October 2025 Revised: 20 December 2025 Accepted: 31 December 2025 Published: 09 January 2026

In this research paper, we utilize an analytical technique to investigate the behavior of the Drinfeld-Sokolov-Wilson equation of arbitrary order. The implemented technique is an adequate composition of the Kharrat-Toma transform and the q-homotopy analysis approach. Here, a regularized form of the Hilfer-Prabhakar derivative of arbitrary order is used to formulate the problem. The Drinfeld-Sokolov-Wilson equation of arbitrary order is utilized to model the dispersive water waves and plays a very significant role in fluid dynamics. The results of the discussed model are presented graphically to show the efficiency and reliability of the obtained results.
Citation: Jagdev Singh, Arpita Gupta, Juan J. Nieto, Moisés Rutkoski. Computational analysis of fractional Drinfeld-Sokolov-Wilson equation associated with regularized form of Hilfer-Prabhakar derivative[J]. Networks and Heterogeneous Media, 2026, 21(1): 1-21. doi: 10.3934/nhm.2026001

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Abstract

In this research paper, we utilize an analytical technique to investigate the behavior of the Drinfeld-Sokolov-Wilson equation of arbitrary order. The implemented technique is an adequate composition of the Kharrat-Toma transform and the q-homotopy analysis approach. Here, a regularized form of the Hilfer-Prabhakar derivative of arbitrary order is used to formulate the problem. The Drinfeld-Sokolov-Wilson equation of arbitrary order is utilized to model the dispersive water waves and plays a very significant role in fluid dynamics. The results of the discussed model are presented graphically to show the efficiency and reliability of the obtained results.

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