Sentence examples for by a fractional operator from inspiring English sources

Two criteria for required by a fractional operator are formulated.

These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1<α≤2.

By the same token, a fractional hazard rate, defined by the application of a fractional operator, implies as well a conventional probability density and its cumulative distribution.

As a result, the movement of animals cannot often obey the rule of normal diffusion, but it obeys Lévy diffusion which is described by a fractional Laplacian operator.

Recently, one [16] presented a new fractional extension of regularized long wave equation by using an Atangana Baleano fractional operator.

In [6, 7], the authors generalized Gâteaux derivative by employing a fractional discrete operator for a Jumarie fractional operator.

All these transformations are obtained by using a fractional calculus operator based on the Pochhammer contour integral.

However, it is very limited to study the stochastic heat equations driven by the mixed fractional operator (Delta+Delta_{alpha}) and fractional Brownian sheet, where (Delta_{alpha}=- -Delta)^{alpha/2}) is the fractional power of the Laplacian.

We develop a numerical method for a generalized nonlocal elastic model, which is expressed as a composition of a Riesz potential operator with a fractional differential operator, by composing a collocation method with a finite difference discretization.

This paper presents the procedure to obtain analytical solutions of Liénard type model of a fluid transmission line represented by the Caputo-Fabrizio fractional operator.

The nonlocal behavior exhibited by a fractional-order differential operator makes it distinct from the integer-order differential operator.