Cristina B. Corcino^1,2, Wilson D. Castañeda Jr.³, Roberto B. Corcino^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 133-151, 2022, DOI:10.32604/cmes.2022.019965

Abstract The tangent polynomials T_n (z) are generalization of tangent numbers or the Euler zigzag numbers T_n. In particular, T_n (0) = T_n. These polynomials are closely related to Bernoulli, Euler and Genocchi polynomials. One of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostoltype polynomials. One of these Apostol-type polynomials is the Apostol-tangent polynomials T_n(z, λ). When λ = 1, T_n (z, 1) = T_n(z). The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez and… More >

Y. A. Amer¹, A. M. S. Mahdy^{1, 2, *}, E. S. M. Youssef¹

CMC-Computers, Materials & Continua, Vol.54, No.2, pp. 161-180, 2018, DOI:10.3970/cmc.2018.054.161

Abstract In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method. The fractional derivatives are described in the Caputo sense. The applications related to Sumudu transform method and Hermite spectral collocation method have been developed for differential equations to the extent of access to approximate analytical solutions of fractional integro-differential equations. More >