Abstract. This paper gives a new formula for the fractional differentiation matrix based on shifted Chebyshev polynomials for solving fractional order ordinary differential equations (FODEs). In addition, we will estimate the error bound of the in the largest element of that matrix. Some numerical examples are included to confirm the accuracy of the new formula and illustrate the practical usefulness of our method.

Received: March 26, 2012

AMS Subject Classification: 65G20, 65L70, 65L09

Key Words and Phrases: fractional differential equations, shifted Chebyshev polynomials, differentiation matrices

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