Sentence examples for fractional calculus method from inspiring English sources

We obtain these transformations by using the fractional calculus method which is a more general method than the beta integral method.

The main objective of the present paper is to show how this simple fractional calculus method to the solutions of some families of fractional differential equations would lead naturally to several interesting consequences, which include (for example) a generalization of the classical Frobenius method.

Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are formulated and proved.

For the part of theoretical results, our basic tools are the theory of fractional calculus, the methods and results for differential inclusions, and several fixed point theorems for multifunctions due to [26, 27].

Nowadays, fractional calculus modeling methods are considered as powerful techniques to handle physical and engineering problems with memory feature and nonlocal property, due to the natural structure of fractional integrals and derivatives making them a global and weak singular integration [10].

In the next section we give some background on fractional calculus and the sinc collocation method.

In Section 4, recent development of the method in fractional calculus is introduced.

This indicates the importance of fractional calculus as an exciting mathematical method for solving various problems in science and engineering.

In this section, we will briefly give some preliminaries of the fractional calculus and the homotopy perturbation method, which will be used in the next sections.

In recent times, one of the most important and useful methods for fractional calculus called fractional complex transform has appeared [33 36].

The methods of fractional calculus, when defined as a Laplace, Sumudu, or Fourier convolution product, are suitable for solving many problems in emerging biomedical research.