W. M. Abd-Elhameed1,2,*, Y. H. Youssri2
CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.3, pp. 1029-1049, 2019, DOI:10.32604/cmes.2019.08378
Abstract This paper is confined to analyzing and implementing new spectral solutions
of the fractional Riccati differential equation based on the application of the spectral tau
method. A new explicit formula for approximating the fractional derivatives of shifted
Chebyshev polynomials of the second kind in terms of their original polynomials is
established. This formula is expressed in terms of a certain terminating hypergeometric
function of the type 4F3(1). This hypergeometric function is reduced in case of the integer
case into a certain terminating hypergeometric function of the type 3F2(1) which can be
summed with the aid of Watson’s identity. Six illustrative… More >
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