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Nonlinear Integro-Fractional Differential Equation, Generalized Taylor's Method, Multinomial Theorem, Collocation Points, Caputo Fractional Derivative.
In this study, generalized Taylor expansion approach formula is developed for solving approximately a Fredholm-Hammerstein type of multi-higher order nonlinear integro- fractional differential equations with variable coefficients under given mixed conditions. The fractional derivative is described in the Caputo sense. Using the collocation points, this new technique depends mainly on transform the nonlinear equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with unknown generalized Taylor coefficients. A best algorithm for solving our equation numerically by applying this process has been developed in order to express these solution, programs are written in MatLab. In addition, the truth and reliability of this method is tested by several illustrative numerical examples are presented to show effectiveness and accuracy of this algorithm.
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