https://doi.org/10.1140/epjp/s13360-026-07622-8
Regular Article
Fractional space–time modeling of MHD mixed convection and entropy generation over a permeable moving surface
1
Faculty of Military Science, Stellenbosch University, Private Bag X2, 7395, Saldanha, South Africa
2
Department of Pure and Applied Mathematics, Saveetha School of Engineering, Saveetha Nagar, Thandalam, 602105, Chennai, Tamilnadu, India
3
School of Mathematics and Statistics, Nanning Normal University, 530100, Nanning, People’s Republic of China
4
Centre for Applied Mathematics of Guangxi, School of Mathematics and Statistics, Nanning Normal University, 530100, Nanning, People’s Republic of China
5
Kuban State Agrarian University, Krasnodar, Russia
a
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Received:
22
November
2025
Accepted:
26
March
2026
Published online:
18
April
2026
Abstract
This study presents a fractional space–time model for magnetohydrodynamic (MHD) mixed convection and entropy generation in boundary layer flow over a moving permeable surface. The governing momentum and energy equations are formulated using Caputo-type time- and space-fractional derivatives of orders 
and 
, allowing the incorporation of memory and nonlocal transport effects that cannot be captured by classical integer-order models. The influences of key parameters, including the magnetic field parameter (0 ≤ 
, Grashof number (0 ≤ Gr ≤ 5), Eckert number (0 ≤ 
, Biot number (0.1 ≤ Bi ≤ 5), and surface suction/injection, are systematically examined. The resulting coupled nonlinear fractional partial differential equations are solved numerically using an Euler wavelet collocation method combined with an implicit finite difference scheme. The results show that increasing fractional orders significantly suppress velocity and temperature fields due to enhanced memory effects, leading to reduced heat transfer rates. Injection intensifies entropy generation by amplifying velocity and thermal gradients, whereas suction stabilizes the boundary layer and minimizes irreversibility. Strong magnetic fields increase entropy production through Joule dissipation while damping fluid motion. The proposed fractional framework provides deeper insight into irreversibility control and thermal optimization in MHD convection systems relevant to energy conversion, thermal management, and porous surface technologies.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
