Sentence examples for engineering fractional from inspiring English sources

During the last two decades, due to its widespread applications in different fields of science and engineering, fractional calculus has attracted the attention of many researchers [1 6].

Due to the extensive applications in various fields such as science and engineering, fractional differential equations attract more and more attention of experts and scholars.

With the development of fractional calculus and the requirement for field applications of physics, mathematics, and chemical engineering, fractional differential equations have attracted great interest in recent years (see, for example, [1 8]).

In various problems of physics, mechanics, and engineering, fractional differential equations and fractional integral equations have been proved to be a valuable tool in modeling many phenomena [1, 2].

With the application of fractional calculus in the field of control engineering, Fractional Order (FO) PID controllers are gaining popularity since it requires a slight modification of the integer order PID controller.

The H-function, which is an extension of the hypergeometric functions (_{p}F_{q}), introduced by Fox [3] (see also [4, 5]), has found various applications in a huge range of problems associated with reaction, reaction diffusion, communication, engineering, fractional differential equations, integral equations, theoretical physics, and statistical distribution theory as well.

During the last five decades, a huge amount of investigators has been worked in almost all fields of sciences and engineering in fractional calculus (fractional derivative and integral) of arbitrary calculus.

In engineering, the fractional order q is often less than 1, so we restrict our attention to (qin 0,1)).

The same methodology was used to optimize several unit operations in food process engineering using fractional factorial experimental designs.

For example, in order to describe certain problems raised in science and engineering, the fractional differential equation is superior to the classical integer one, especially in the fields of biology, physics, mechanics, ecological engineering, finance and other fields which propose the process of memory and genetic properties.

Nowadays the number of scientific and engineering problems involving fractional calculus is already very large and still growing.