Sentence examples similar to tool for fractional from inspiring English sources

Recently, Benkhettou et al. developed a conformable fractional calculus theory on arbitrary time scales [48], and established the basic tools for fractional differentiation and fractional integration on time scales.

Generalized Word Length Pattern (GWLP) is an important and widely-used tool for comparing fractional factorial designs.

This work shows that the LHAM is a very efficient tool for solving linear fractional partial differential equations considering fractional operators of Liouville-Caputo and Caputo-Fabrizio type.

This work shows that the HPTM method is an efficient tool for solving nonlinear fractional partial differential equations considering the fractional operator of Caputo-Fabrizio type.

Lemma 2.1, Lemma 2.2, and Lemma 2.4 provide powerful tools for exploring fractional-order differential equations.

In recent years, the fractional calculus is considered as the best tool for the generalizations of fractional differential equations [1 5].

The method of a (u_{0} -positive operator is an important tool in boundary value problems for fractional differential equations.

Hence, critical point theory is the main tool for finding solutions to fractional discrete nonlinear equations.

It is to be considered an additive tool for the field of fractional theory and computations.

Thus the analytical method HPM is a useful tool for solving the nonlinear fractional equations.

Presently, many mathematicians apply this approach and operator tools to investigate various problems for fractional partial differential equations which appear in applied problems (see, e.g., [13 20] and the references therein).