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Abstract
The objective of the present work is to introduce a computational approach employing Chebyshev Tau method for approximating the solutions of constant coefficients systems of multi-order fractional differential equations. For this purpose, a series representation for the exact solutions in a neighborhood of the origin is obtained to monitor their smoothness properties. We prove that some derivatives of the exact solutions of the underlying problem often suffer from discontinuity at the origin. To fix this drawback and design a high order approach a regularization procedure is developed. In addition to avoid high computational costs, a suitable strategy is implemented such that approximate solutions are obtained by solving some triangular algebraic systems. Complexity and convergence analysis of the proposed scheme are provided. Various practical test problems are presented to exhibit capability of the given approach.
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