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Jocemar Q. Chagas

Publications and source records attributed to Jocemar Q. Chagas.

4 recordsLinked to original sources
arXiv2023

Fractional Finite Sums Theory: a motivation and some new results

This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a function). Examples of the essences of functions are presented, including the Bernoulli numbers, which are obtained as essences of the functions $f(x)=x^a$, $a \in \mathbb{N}^*$. Based on the new results, we can expand the comprehension of the Euler-Maclaurin summation formula for a real number instead of only considering natural numbers. Moreover, we utilize the concept of the essence of a function to propose a new regularization method for divergent series.

math.NT↗
arXiv2020

A numerical method for a class of nonlinear fractional advection-diffusion equations

In this note, a numerical method based on finite differences to solve a class of nonlinear advection-diffusion fractional differential equation is proposed. The fractional operator considered here is the fractional Riemann-Liouville derivative or the fractional Riesz derivative of order $α$. The consistency and unconditionally stability of the method are shown. Finally, an example of application of this method is presented.

math.AP↗
arXiv2017

Some properties for the Steklov averages

We derive and present a collection of properties about the Steklov averages, including some results about the derivation with respect to spatial variables, and with respect to time, and a form of the fundamental theorem of the calculus.

math.AP↗