Sentence examples for derivatives by using from inspiring English sources
A new fourth-order difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted Grünwald formulae combining the compact technique.
The method is based on approximating functions and their derivatives by using the Whittaker cardinal function.
Very recently, Gu and Trujillo [18] investigated a class of evolution equations involving the Hilfer fractional derivatives by using Mittag-Leffler functions.
In the "evolution stage", we update by means of a procedure similar to that of Cauchy Kovaleskaya, the discrete variable and its derivatives, by using the information brought by each simple wave.
The comparatively FTIR analysis of both the samples revealed that unsaturated hydrocarbon fragments were transformed in to the oxygenated products which were confirmed by GC/MS analysis and identified as a phytol, free fatty acids and silica derivatives by using NIST library.
Sugars were analyzed as trimethylsilyl derivatives by using gas chromatography (22).
The shape derivatives are derived by using a Lagrangian function and the adjoint method.
Recently, Klimek investigated existence and uniqueness of the solution of sequential fractional differential equations with Hadamard derivative by using the contraction principle in [16].
Romero et al. [20] introduced a new fractional operator called the k-Riemann-Liouville fractional derivative by using gamma k-function.
Recently, Allahviranloo et al. [14] and Hoa [15] independently introduced the concept of Caputo gH-derivative by using the generalized Hukuhara difference (or gH-difference).
Ahmadi et al. investigated the Laplace transform formula on the fuzzy nth-order derivative by using the strongly generalized differentiability concept in [17].
