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A Novel Crossover Variable Order (Deterministic- Stochastic) Lung Cancer and Tumor-Immune System Interaction: Numerical Simulations |
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PP: 73-86 |
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doi:10.18576/pfda/110106
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Author(s) |
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Seham M. Al−Mekhlafi,
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Abstract |
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| The tumor-immune interaction model related to lung cancer by applying the fractional variable-order Brownian motion and hybrid variable-order fractional piecewise derivatives are presented for the first time in this paper. The variable order fractional derivative of the Caputo proportional constant is applied to extend the deterministic model, and the variable order fractional Brownian motion is applied to extend the stochastic differential equations. A parameter ζ is presented to be consistent with the physical model problem. The stability of the proposed model is discussed. New numerical algorithms are improved to study the proposed model. These techniques are the modified nonstandard Euler Maruyama approach to study the stochastic model and the constant proportional Caputo non-standard fifth step Adams-Bashfourth method to study numerically the deterministic model of variable order derivative. Several numerical experiments verify the method’s efficiency and support the theoretical results.
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