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Start Over Topic fractional derivative Language spanish; castilian Publication Type Periodicals
3 results

1. Gaussian integral by Taylor series and applications

Author

Lázaro Lima de Sales, Jonatas Arizilanio Silva, Eliângela Paulino Bento de Souza, Hidalyn Theodory Clemente Mattos de Souza, Antonio Diego Silva Farias, and Otávio Paulino Lavor

Subjects
Gaussian Integral, Special Functions, Fractional Derivative, Special aspects of education, LC8-6691, Mathematics, QA1-939
Abstract

In this paper, we present a solution for a specific Gaussian integral. Introducing a parameter that depends on a n index, we found out a general solution inspired by the Taylor series of a simple function. We demonstrated that this parameter represents the expansion coefficients of this function, a very interesting and new result. We also introduced some Theorems that are proved by mathematical induction. As a test for the solution presented here, we investigated a non-extensive version for the particle number density in Tsallis framework, which enabled us to evaluate the functionality of the method. Besides, solutions for a certain class of the gamma and factorial functions are derived. Moreover, we presented a simple application in fractional calculus. In conclusion, we believe in the relevance of this work because it presents a solution for the Gaussian integral from an unprecedented perspective.

Published
2021
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2. Descripción de la clase de Nikolski\u\i-Besov disminuyendo su parámetro de suavidad, mediante derivadas fraccionarias débiles

Author

ENRÍQUEZ, FRANCISCO and PÉREZ, JHON

Subjects
Nikolski\u\i-Besov spaces, Espacios de Nikolski\u\i-Besov, núcleo de Poisson, integral de Poisson, Fractional derivative, Poisson kernel, derivada fraccionaria, Poisson integral
Abstract

Los espacios de Nikolskii-Besov Bpqα\big(Rn\big)≡ Bpqα, 1≤ p,\,q≤∞, α>0, se han descrito recientemente con ayuda de las derivadas fraccionarias de Caputo. Usando el concepto de derivada fraccionaria débil, en el presente trabajo se reduce la caracterización de Bpqα al caso Bpqγ, donde γ es cualquier número positivo estrictamente menor que α. The Nikolski\u\i-Besov spaces Bpqα\big(Rn\big)≡ Bpqα, 1≤ p,\,q≤∞, α>0, recently were described using the Caputo's fractional derivative. Using the concept of weak fractional derivative, in this paper we reduces the characterization of Bpqα to the case Bpqγ, where γ is any positive number strictly less than α.

Published
2013

3. Description of the nikolskii-besov class decreasing its smoothness parameter using weak fractional derivatives

Author

Enríquez, Francisco and Pérez, Jhon

Subjects
Espacios de Nikolskii-Besov, 26A16, Nikolskii-Besov spaces, núcleo de Poisson, integral de Poisson, Fractional derivative, Poisson kernel, derivada fraccionaria, 26A33, Poisson integral
Abstract

The Nikolskii-Besov spaces Bpqα(Rn)≡ Bpqα, 1≤ p, q≤∞, α and gt;0, recently were described using the Caputo's fractional derivative. Using the concept of weak fractional derivative, in this paper we reduces the characterization of Bpqα to the case Bpqγ, where γ is any positive number strictly less than α. Los espacios de Nikolskii-Besov Bpqα(Rn)≡ Bpqα, 1≤ p, q≤∞, α and gt;0, se han descrito recientemente con ayuda de las derivadas fraccionarias de Caputo. Usando el concepto de derivada fraccionaria débil, en el presente trabajo se reduce la caracterización de Bpqα al casoBpqγ, donde γ es cualquier número positivo estrictamente menor que α.

Published
2013