Revision as of 14:11, 11 February 2026

Abstract

Fractal-fractional derivatives generalize both traditional and fractional differentiation approaches by integrating memory effects with fractal properties. This mathematical framework is especially valuable for describing complex systems in which conventional continuum mechanics becomes inadequate, particularly in scenarios involving porous or discontinuous structures. This research investigates the behavior of a non-linearWalter’s-B fluid subjected to time-varying thermal and concentration conditions. Beyond the extended derivative formulation, the analysis incorporates phenomena including first-order chemical reactions, radiative heat transfer, Joule heating, Soret effect, and viscous dissipation. Thesystem is also subjected to a transverse magnetic field with magnitude B0.The fluidmodel is initially formulated through traditional constitutive equations and subsequently generalized using a fractal-fractional operator. Solutions to this extendedmodel are computed employing ameshfree numerical approach utilizing localized radial basis functions (LRBF), which eliminates the requirement for structured grids and improves precision when addressing intricate geometries.The computational outcomes, displayed through graphical representations, illustrate how the fractional and fractal parameters influence the rheological characteristics of the Walter’s-B fluid. These findings establish that adjusting these parameters enables retrieval of classical, fractional, and fractal formulations as particular instances within this comprehensive mathematical structure.

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