The need for fractional order differential equations stems in part from the fact that many phenomena cannot be modeled by differential equations with integer derivatives.
The need for fractional order differential/integral equations stems in part from the fact that many phenomena cannot be modeled by differential/integral equations with integer derivatives.
According to commentary in the Red Book, the twenty-cent piece failed because "the public was confused over the coin's similarity to the quarter dollar, which was better established as a foundation of American commerce", that fractional currency satisfied the need for small change in the East, and because "the twenty-cent piece was essentially just a substitute for two dimes".
Next, we will derive some properties of the h-fractional function, which we need for the proofs of the main results, but which are also of independent interest.
The method gives an analytical solution in the form of convergent multi-fractional power series without the need for linearization, perturbation, or discretization of the variables.
As a final result, a table is presented demonstrating the integer and fractional bit range needed for each EKF variable.
The application of fractional factorial designs and statistical methods, which consider the need for replicating experiments and resources, may reduce experimental efforts [ 40, 73, 74].
Our simulation shows that the fractional model has great potential to describe the real problem without the need for adjustment of parameters obtained in the field research.
For both polymers, superposing the curves of fractional recovery vs. setting time at different temperatures produce satisfactory master curves, without the need for vertical shifting of the data.
This tool estimates fractional fetal DNA concentration directly from massively parallel sequencing on DNA in maternal plasma, eliminating the need for prior genotype information.
Finally, acute lung injury was defined as an arterial oxygen tension/fractional inspired oxygen ratio below 300 mmHg and need for mechanical ventilation.
