This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the...

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful effective type of inequality. The main findings by using integrable functions generalized fractional integral operators many existing results as well iterating the Chebyshev special cases.

We compare the convergence behavior of best polynomial approximations and Legendre Chebyshev projections derive optimal rates for analytic differentiable functions in maximum norm. For functions, we show that approximation degree n is better than projection same by a factor $$n^{1/2}$$ . such as piecewise fractional smoothness, however, only some constant factors. Our results provide new insig...

in this paper we apply hybrid functions of general block-pulse‎ ‎functions and legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (fdes)‎. ‎our approach is based on incorporating operational matrices of‎ ‎fdes with hybrid functions that reduces the fdes problems to‎ ‎the solution of algebraic systems‎. ‎error estimate that verifies a‎ ‎converge...