Best Approximation of the Fractional Semi|Derivative Operator by ...

Fractional derivatives? Irrational derivatives (such as eth or Pith ...

Remember that the Laplace transform of the derivative is multiplication by s in the Laplace domain. For each of these operators above, the ...

View of Innovative Method for Computing Approximate Solutions of ...

In this equation, the time or space derivative is replaced by a fractional derivative. The fractional derivative describes the non-local properties of a wave, ...

Some Results in Grűnwald-Letnikov Fractional Derivative and its ...

Keywords: Best Approximation, Bernstein-Chlodowsky polynomials, Grűnwald-Letnikov derivatives, Fractional differential equations. 1. Introduction. The topic of ...

Fractional‐Derivative Approximation of Relaxation in Complex ...

The parameters in the models are the order of the equation, the coefficients in it, and, when necessary, the initial conditions. The Caputo ...

Approximation of Two-Dimensional Time-Fractional Navier-Stokes ...

In this section, we use the AB fractional derivative operator to examine the two-dimensional TFNS equation by using NITM and HPTM with the ...

Finite difference - Wikipedia

If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in ...

Study on a fractional-order controllers based on best rational ...

This paper presents a rational approximation method for fractional calculus operators s±αin the given frequency range and the error, ...

Application of Newton's polynomial interpolation scheme for variable ...

This paper, offers a new method for simulating variable-order fractional differential operators with numerous types of fractional ...

Applications of variable-order fractional operators: a review - PMC

The theory of generalized VO operators and the corresponding VO equations has been addressed in [59–61]. It is shown in [62] that the solutions to VO fractional ...

APPROXIMATION OF THE ERDÉLYI–KOBER OPERATOR ... - jstor

The obtained accuracy is very good and the fitting with the data is decent. 2. Main equation and the approximation of the fractional derivative. In this section ...

Numerical approximation of fractional powers of elliptic operators

155 Citations · Comparison analysis on two numerical methods for fractional diffusion problems based on rational approximations of $t^{\gamma}, \ 0 \le t \le 1$.

FRACTIONAL CALCULUS AND SPECIAL FUNCTIONS

The Grünwald-Letnikov approximation for the fractional Liouville-Weyl derivatives ... Balakrishnan, Fractional powers of closed operators and the semi-groups.

Numerical Methods in Fractional Calculus - ScholarWorks

a method to numerically evaluate a fractional derivative of a function at a point. ... Now let us look at the third order derivative approximation. By ...

S. B. Stechkin, “Best approximation of linear operators”, Mat. Zametki ...

... Differentiation Operator in the Uniform Norm on the Half-Line”, Math. ... Surkov, “Approximate calculation of the Caputo-type fractional derivative from ...

Fractional vs. Ordinary Control Systems: What Does the ... - RiuNet

The FOTF approximate fractional differential operators by means of a discretization of the Grünwald–Letnikov definition of noninteger derivative ...

A numerical approximation for the Caputo-Hadamard derivative and ...

Then, we discretize the time-fractional derivative using the derived L1 scheme and approximate the spatial derivative by the local discontinuous Galerkin (LDG) ...

ON THE BEST APPROXIMATION OF THE DIFFERENTIATION ...

Gabushin V.N. On the best approximation of the differentiation operator on the half-line // Math. Notes. 1969. Vol. 6. P. 804–810.

A Caputo fractional derivative of a function with respect to another ...

The idea is to approximate the fractional derivative by a sum, which depends only on the derivatives of integer order. This was already done for the Riemann– ...

Best Approximations by Fractions | Mathematics Experiments

Best Approximations by Fractions · A Hybrid Approximation Method for Integer Order Approximate Realization of Fractional-Order Derivative Operators · FRACTIONAL ...

(PDF) Approximation of fractional integrals by means of derivatives

We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus.