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                    کلیدواژهها
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                     Chebyshev polynomials, fixed point, Legendre polynomials, numerical solution,
k-dimensional system of multi-term fractional differential equations. 
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                    چکیده
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                     First, we investigate the existence and uniqueness of solution for a k-dimensional system
of multi-term fractional integro-differential equations. Also, we apply shifted Chebyshev and
shifted Legendre polynomials to obtain an approximation solution for the k-dimensional system.
Finally, we provide some examples illustrating the presented methods. 
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