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Abstract
This research article intends to utilize results on Lie symmetry analysis, explicit series solutions and conservation laws for the time-fractional Zakharov-Kuznetsov (q,p,r) equation in three-dimensional space. Such a fractional equation yields the mathematical model which describes an occurrence of stationary spatial stripe modalities in a three-dimensional system in the framework of the theory of conservation laws. The governing equation is solved analytically by the power series method, where the total derivative in the sense of Riemann-Liouville type. Simulation results are systematically validated through a series of test cases. Strong evidence shows that the model and the method are conservative and robust.
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