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Univariate right fractional polynomial high order monotone approxi mation

Anastassiou G. A.

Demonstratio Mathematica

2016

Vol. 49, nr 1

1--10

Let (…) and let L* be a linear right fractional differential operator such that L*(f) ≥ 0 throughout [-1, 0]. We can find a sequence of polynomials Qn of degree ≤ n such that L*(Qn)≥ 0 over [-1, 0], furthermore f is approximated right fractionally and simultaneously by Qn on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for f(r).

The Dirichlet problem for the time-fractional advection-diffusion equation in a half-space

Povstenko Y., Klekot J.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 2

73--83

The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a half-space. The fundamental solution to the Dirichlet problem and the solution of the problem with constant boundary condition are obtained using the integral transform technique. The numerical results are illustrated graphically.