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Palabras claves o descriptores: FRACTIONAL CALCULUS (Comienzo)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: López-Marcos, J.
Título: A Difference Scheme for a Nonlinear Partial Integrodifferential Equation
Páginas/Colación: pp. 20-31
Url: Ir a http://locus.siam.org/SINUM/volume-27/art_0727002.htmlhttp://locus.siam.org/SINUM/volume-27/art_0727002.html
Siam Journal on Numerical Analysis Vol. 27, no. 1 February 1990
Información de existenciaInformación de existencia

Palabras Claves: Palabras: FINITE DIFFERENCES FINITE DIFFERENCES, Palabras: FRACTIONAL CALCULUS FRACTIONAL CALCULUS, Palabras: INTEGRODIFFERENTIAL EQUATIONS INTEGRODIFFERENTIAL EQUATIONS

Resumen
RESUMEN

RESUMEN

 

A difference method for the numerical integration of a nonlinear partial integrodifferential equation is considered. The integral term is treated by means of a convolution quadrature suggested by Lubich. Some results from Lubich’s discretized fractional calculus play a crucial role in proving consistency. The verification of stability and convergence is based on the nonnegative character of the real quadratic form associated with the convolution quadrature. A stability result is derived that is applicable to equations and numerical methods far more general than those treated in this paper.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Hu, Yaozhong ; Nualart, David
Título: Rough path analysis via fractional calculus
Páginas/Colación: pp. 2689-2718
Fecha: May 2009
Transactions of the American Mathematical Society Vol. 361, no.5 May 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: CONVERGENCE RATE CONVERGENCE RATE, Palabras: DIFFERENTIAL EQUATION DIFFERENTIAL EQUATION, Palabras: FRACTIONAL CALCULUS FRACTIONAL CALCULUS, Palabras: INTEGRAL INTEGRAL, Palabras: INTEGRATION BY PARTS INTEGRATION BY PARTS, Palabras: ROUGH PATH ROUGH PATH, Palabras: STABILITY STABILITY, Palabras: STOCHASTIC DIFFERENTIAL EQUATION STOCHASTIC DIFFERENTIAL EQUATION, Palabras: WONG-ZAKAI APPROXIMATION WONG-ZAKAI APPROXIMATION

Resumen
For about twenty five years it was a kind of folk theorem that complex vector-fields defined on (with open set in ) by

Using fractional calculus we define integrals of the form $ \int_{a}^{b}f(x_{t})dy_{t}$, where $ x$and $ y$are vector-valued Hölder continuous functions of order $ \beta \in (\frac{1}{3}, \frac{1 }{2})$and $ f$is a continuously differentiable function such that $ f^{\prime }$is $ \lambda $-Hölder continuous for some $ \lambda >\frac{1}{ \beta }-2$. Under some further smooth conditions on $ f$the integral is a continuous functional of $ x$, $ y$, and the tensor product $ x\otimes y$with respect to the Hölder norms. We derive some estimates for these integrals and we solve differential equations driven by the function $ y$. We discuss some applications to stochastic integrals and stochastic differential equations

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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