Sentence examples for by using fractional calculus from inspiring English sources

Fractional-order PID controllers described by using fractional calculus are the most common and useful algorithms in control system engineering.

We establish fractional integral and derivative formulas by using fractional calculus operators involving the extended generalized Mathieu series.

Jajarmi et al. [22] analyzed a hyperchaotic financial system and its chaos control and synchronization by using fractional calculus.

The results are obtained by using fractional calculus, Hausdorff measure of noncompactness, and the multivalued fixed point theorem.

By using fractional calculus, the properties of characteristic solution operators, Mönch's fixed point theorem via MNC, we have found the existence results.

This is due to the fact that a realistic model of a physical phenomenon has a dependence not only on the time instant, but also the previous time history can be successfully described by using fractional calculus [14 18].

Fractional-order PID (FOPID) controller is a generalization of traditional PID controller using fractional calculus.

Fractional-order PID (FOPID) controller is a generalization of standard PID controller using fractional calculus.

Fractional order PID (FOPID) controllers are introduced as a general form of classical PID controllers using fractional calculus.

Many mathematicians and applied researchers have tried to model real processes using fractional calculus [10 16].

Sarikaya et al. [12] developed a new generalization of Hermite-Hadamard-type inequality using fractional calculus approach.