Sentence examples for use the general solution from inspiring English sources

In the following discussion we will use the general solution (3.25) and its fractional Caputo derivative ^{mathrm{C}}_{0} D^{beta} y(t) = A t^{-beta} E_{alpha, 1-beta}bigl -lambda t^{alpha}bigr) + B t^{1-beta}bigl -lambda-beta }bigl(-lambda t^{alpha}bigr).

Using the general solution, analytical expressions of thermal distortion and associated internal forces for commonly used end supports are obtained.

Finally, an application to forming process design problems is discussed and a simple example is illustrated using the general solution.

The remaining solutions can be obtained using the general solution of the differential equation (3.3) and then imposing the initial condition (3.4).

In this paper, based on the anomalous diffusion phenomena that also have the long-tail behavior, we developed a new fractional decline curve (FDC) model with three fitting parameters using the general solution of the fractional diffusion equations, which is a special case of so-called Mittag-Leffler function.

For free vibration, an analytic form of frequency equation is obtained by using the general solution expressed in terms of some initial parameters at one end of the arch; while for forced vibration, the system's response is obtained analytically by solving a set of algebraic equations with only three unknowns.

Step 4. Solving the equations system in Step 3, and using the general solutions of (1), we can construct a variety of exact solutions for (7).

The binary (0/1) integer varibles of the non-convex MINLP problem make it impossible to use the general purpose algorithms for solution.

A potential solution is to use the general automated system to perform the initial selection of articles that are most likely to be 'useful' and articles that are most likely to be 'non-useful' for manual classification.

According to the physical model, the transmission and reflection matrices (TRM) method was used, and the general solutions for the stresses and displacements of the layered system subjected to dynamic double-circular loads at its surface were obtained.

Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions.