Sentence examples for derivative definition from inspiring English sources

For these reasons, we adopt the Caputo fractional derivative definition in this work.

In order to estimate the fractional Laplacian operator term in our problems, we need the following symmetric fractional derivative definition.

Also, Caputo type derivative definition and its properties in the crisp sense is considered in this section.

As demonstrated in [3], and whatever the fractional derivative definition used (excepted Caputo's definition but this last one is not physically acceptable [14]), the value of vector at initial time in (2.2) is not enough to predict the future behavior of the system.

Section 2 is devoted to a brief review of the fractional derivative definitions and fractional forms.

Section 4.2 of the 2003 International Swaps and Derivatives Association's credit derivatives definition lists seven categories that could set off a bankruptcy credit event and thus a payout from a protection seller.

We summarize some of the features, structures, and functions of the stem cell niches in these ectodermal derivatives; definition of the basic elements of the stem cell niches in these organs will provide guiding principles for identification and characterization of the niche in similar systems.

In this general time-scale setting, represents the delta (or Hilger) derivative [13, Definition 1.10], (2.2).

In Section 2, we give a brief history and properties of the fractional derivative order definition.

To this end, let be the vector of partial derivatives of with respect to the elements of, where denotes the matrix derivative operator[28, Definition 2].

Here I α stands for the standard Riemann-Liouville fractional integral of order α > 0 and D α denotes the Riemann-Liouville fractional derivative as Definition 2.1.