Generally, the field cases reviewed show the robustness of the statistical 'pressure' and numerical density derivatives applicable in pressure transient analysis.
The fluctuations are expressed in terms of integrals of the Mathieu cosine and sine functions and their derivatives, applicable for arbitrary values of the dimensionless trap parameters b and q.
Because of these properties, l-AA derivatives were applicable in cosmetics and medicine [12, 13].
The main concern of the paper thus focuses on the Caputo derivative of order (alpha>0), which is rather applicable in real application.
Classical optimization methods, based on derivatives, are not applicable because often derivative information is not available and is too expensive to approximate through finite differencing.
As traditional kinetic-energy-based orthogonality conditions, based on displacement or temporal derivatives, are not applicable a new (approximate) strain-energy-based orthogonality condition is developed.
Fractional differential equations with both left and right fractional derivatives are also applicable to many fields, such as the extremal problems of fractional Euler-Lagrange equations [6, 7] and the optimal control theory for functionals involving fractional derivatives [8].
The authors declare that they are pursuing patents for the methods and uses and, when applicable, the elicitors, inhibitors, and derivatives or their combination generated in the name of CIATEJ AC, with E. Prado Montes de Oca et al., as inventors.
The adoption of FDTD efficiently overcomes the difficulties arising from the existing calculation methods' requirements for the radiation analytical formula of some complex antennas, which makes the existing second-derivative method more applicable in engineering.
Hence, algorithms that rely on the first- or second-order derivatives will not be applicable in this case.
