TY - EJOU
AU - Abd-Elhameed, W. M.
AU - Youssri, Y. H.
TI - Explicit Shifted Second-kind Chebyshev Spectral Treatment for Fractional Riccati Differential Equation
T2 - Computer Modeling in Engineering \& Sciences
PY - 2019
VL - 121
IS - 3
SN - 1526-1506
AB - 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 _{4}*F*_{3}(1). This hypergeometric function is reduced in case of the integer
case into a certain terminating hypergeometric function of the type _{3}*F*_{2}(1) which can be
summed with the aid of Watsonâ€™s identity. Six illustrative examples are presented to ensure
the applicability and accuracy of the proposed algorithm.
KW - Chebyshev polynomials of the second kind
KW - spectral methods
KW - linearization formula
KW - hypergeometric functions
DO - 10.32604/cmes.2019.08378