The Hadamard fractional derivative, introduced by Hadamard in 1892 [12], differs from the Riemann-Liouville and Caputo derivatives in the sense that the kernel of the integral (in the definition of Hadamard derivative) contains a logarithmic function of arbitrary exponent.
This fractional derivative differs from the other ones in the sense that the kernel of the integral (in the definition of the Hadamard derivative) contains a logarithmic function of an arbitrary exponent.
This derivative differs from the aforementioned derivatives in the sense that the kernel of the integral in the definition of the Hadamard derivative contains a logarithmic function of arbitrary exponent.
The final form of this formula contains a coefficient function of stoichiometry, which was derived by matching the theoretical and numerical predictions.
These patterns support the interpretation that swamp patches at Barrington Tops contain a functioning but fragile metapopulation of M. fuscus.
A first-order component (y'+r x,y)=0) exists if r is a solution of begin{aligned} r_x-rr_y-R x,y,-r_x-rr_y-R xigned} (2)its gener_x-rr_y-R x contains an undetermined function of x and y.
However, the FFC contains an inverse function of the power amplifier, whose errors and variations can result in gain and phase differences and changes between the output voltage of the controller and the actual output current of the power amplifier.
Each of the obtained solutions, namely hyperbolic function solutions, trigonometric function solutions and rational function solutions, contain an explicit function of the variables in the considered equation.
This inbred line contains a loss-of-function p1-ww allele.
The rsp2 mutant contains a loss-of-function allele of dihydrodipicolinate synthase2[ 11], which is the key enzyme in lysine biosynthesis.
