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چکیده
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This study introduces a novel fractional-order model for analyzing electrohydrodynamic flow governed by a singular nonlinear differential system in a circular cylindrical conduit. The model incorporates the 𝜓-tempered fractional derivative, which effectively captures the non-local and memory-dependent dynamics that classical integer-order models fail to represent. To overcome the associated computational challenges, we develop an innovative numerical framework combining the fractional-order Genocchi neural network with a spectral collocation method. A key component of this framework is the formulation of a new integral operator for the 𝜓-tempered fractional integral, derived using the Fejér quadrature formula, which ensures accurate and stable numerical integration. The proposed hybrid scheme successfully reduces the original fractional differential system to a tractable set of algebraic equations, facilitating high-precision approximation of solutions. The framework is employed to investigate the impact of critical physical parameters, such as the degree of nonlinearity, the Hartmann number, and the order of the fractional derivative, on the flow’s velocity profile. Moreover, the method’s theoretical rigor is supported by error analysis in the Sobolev norm which confirms the robustness and efficiency of the method for simulating complex fractional-order EHD phenomena.
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