Sentence examples for a class of evolution from inspiring English sources

In this paper, we get a new form equivalent integral equation for a class of evolution equations of fractional order with nonlocal conditions on the half-line.

Very recently, Gu and Trujillo [18] investigated a class of evolution equations involving the Hilfer fractional derivatives by using Mittag-Leffler functions.

The control design, well-posedness, and stability analysis are based on two Lyapunov-type theorems developed for a class of evolution systems in Hilbert space.

It is different from those obtained in the existing literature, and according to it, we investigate a class of evolution equations of fractional order with nonlocal conditions on the half-line.

We will conclude the section with a sample application of these techniques to the global (in time) existence of solutions for a class of evolution equations that include the subRiemannian total variation flow [14].

In particular, Gu and Trujillo [5] investigated a class of evolution equations, textstylebegin{cases} D^{nu,mu}_{0+}u(t)=Au(t)+f t,u(t)),& tin 0,b], I^{ 1-nu)(1-mu)}_{0+}u(0)=u_{0}, end{cases} wI^{ 1-nuer fractional derivatives, by the Laplace transform and density function; they first gave the mild solution definition.

Based on an equivalent integral equation of a new type for a class of fractional evolution equations, which is different from those obtained in the existing literature, the paper investigates a class of fractional evolution equations with nonlocal conditions on infinite interval.

In this paper, an equivalent integral equation of a new type for a class of fractional evolution equations is obtained.

For the existence of solutions for a class of nonlinear evolution equations with monotone perturbations, one can refer to [9 11].

In general, existence of solutions for a class of nonlinear evolution equations of second order is proved by studying a full discretization.

We study analyticity with respect to time of the solutions to a class of nonlinear evolution equations in Banach space.