Higher-dimensional physical models with multimemory indices: analytic solution and convergence analysis.

The purpose of this work is to analytically simulate the mutual impact for the existence of both temporal and spatial Caputo fractional derivative parameters in higher-dimensional physical models. For this purpose, we employ the -Maclaurin series along with an amendment of the power series technique. To supplement our idea, we present the necessary convergence analysis regarding the -Maclaurin series.

Development of spreading symmetric two-waves motion for a family of two-mode nonlinear equations.

In this work, a functional operator extracted from Korsunsky's technique is used to produce new two-mode nonlinear equations. These new equations describe the motion of two directional solitary-waves overlapping with an increasing phase-velocity and affected by two factors labeled as the dispersion and nonlinearity coefficients. To investigate the dynamics of this two-mode family, we construct the two-mode KdV-Burgers-Kuramoto equation (TMKBK) and two-mode Hirota-Satsuma model (TMHS).

Convergence and norm estimates of Hermite interpolation at zeros of Chevyshev polynomials.

In this paper, we investigate the simultaneous approximation of a function () and its derivative [Formula: see text] by Hermite interpolation operator [Formula: see text] based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil (Numer Funct Anal Optim 21(5-6): 579-588, 2000), while others agrees with Pottinger's results (Pottinger in Z Agnew Math Mech 56: T310-T311, 1976).