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Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model

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2021

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Abstract

This manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.

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Fractional Operator With the Non-Singular Kernel, Numerical Approximation, Stability Analysis, Convergence Analysis, Tumor Model, Chaos

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Arshad, Sadia...et al. (2021). "Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model", PHYSICA SCRIPTA, Vol. 96, No. 12.

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PHYSICA SCRIPTA

Volume

96

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12

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