Advanced modelling techniques for magnetohydrodynamic Casson fluid squeezing flow via generalized fractional operators with neural network scheme

Abstract

Abstract This paper aims to simulate and examine the unstable squeezed circulation of fractional-order (FO) magnetohydrodynamic (MHD) Casson fluid via a permeable medium. The Casson fluid system performs an essential role in comprehending the characteristics of non-Newtonian fluids, including toothpaste, condiments, printing substances and plasma circulation. The outcomes of this investigation are significant because previous research has not addressed the unsteady circulation of Casson fluid in a fractional nonsingular kernel and neural network-based stochastic context, considering the indicated consequences. An exceptionally dynamic ordinary differential equation is produced by using fractional calculus in combination with similarity transforms. After that, the predicted problem is addressed employing an amalgam of the Laplace transform in the Caputo-Fabrizio, modified Atangana-Baleanu-Caputo fractional derivatives operators, and the $q$-homotopy analysis transform method, accompanied by no-slip boundary requirements. The responses and oversights at various points in the FOs are scrutinized, along with previous findings, in order to ensure reliability. In terms of precision, $q$-HATM findings outperform other outcomes that are accessible in research. The focus of this research is on the influence of FOs on the velocity distribution, skin friction coefficient (SFC) and practices of relevant fluid factors. To find out how relevant fluid components affect the velocity distribution and SFC, an extensive, qualitative and visual evaluation is carried out. It was discovered through evaluation that the FO shows an analogous impact for both positive and negative squeezing numbers. Additionally, as the FO increases, SFC reduces. Analysis revealed that the FO exhibits a similar effect with regard to positive and negative compression numbers. Furthermore, SFC decreases with increasing FOs. Additionally, a highly effective stochastic method employing artificial neural networks (ANNs) and a back-propagated Levenberg-Marquardt (BPLM) procedure is generated to explore the effect of different parameter modifications on the SFC, velocity distribution, as well as various fluid factors. Multiple effectiveness measures were developed according to mean absolute deviations (MAD), erroneous Nash-Sutcliffe effectiveness (ENSE), and Theil's inequity coefficient (TIC) in order to verify the preciseness, productivity, and computing cost of the ANN-BPLM algorithms. The outlined scheme's analytical findings are verified through comparison using numerical outcomes obtained through the $q$-HATM, artificial intelligence strategies like NARX-LM, and the least squares methodology (LSM). The outcomes indicate the resilience and accuracy of the layout procedure by demonstrating that the average percentage of errors in our proposed outcomes in terms of ENSE, TIC, and MAD is nearly zero.