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 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 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