The Rayleigh–Stokes Problem for a Heated Generalized Second-Grade Fluid with Fractional Derivative: An Implicit Scheme via Riemann–Liouville Integral. (6th May 2022)

• Record Type: Journal Article
• Authors: Ganie, Abdul Hamid; Saeed, Abdulkafi Mohammed; Saeed, Sadia; Ali, Umair
• Other Names: Irfan Muhammad Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2022(2022)
• Publication Date: 2022-05-06
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2022/6948461
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : The goal of this study is to use the fast algorithm to solve the Rayleigh–Stokes problem for heated generalized second-grade fluid (RSP-HGSGF) with Riemann–Liouville time fractional derivative using the fast algorithm. The modified implicit scheme, which is formulated by the Riemann–Liouville integral formula and applied to the fractional RSP-HGSGF, is proposed. Numerical experiments will be carried out to demonstrate that the scheme is simple to implement, and the results will reveal the best way to implement the suggested technique. The proposed scheme's stability and convergence will be examined using the Fourier series. The method is stable, and the approximation solution approaches the exact solution. A numerical demonstration will be provided to demonstrate the applicability and viability of the suggested strategy.