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Almost-distribution cosine functions and integrated cosine functions

Pedro J. Miana (2005)

Studia Mathematica

We introduce the notion of almost-distribution cosine functions in a setting similar to that of distribution semigroups defined by Lions. We prove general results on equivalence between almost-distribution cosine functions and α-times integrated cosine functions.

An algebraic derivative associated to the operator D δ

V. Almeida, N. Castro, J. Rodríguez (2000)

Banach Center Publications

In this paper we get an algebraic derivative relative to the convolution ( f * g ) ( t ) = 0 t i f ( t - ψ ) g ( ψ ) d ψ associated to the operator D δ , which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Kilbas, Anatoly, Repin, Oleg (2010)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness...

An analysis of the stability boundary for a linear fractional difference system

Tomáš Kisela (2015)

Mathematica Bohemica

This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference...

An Expansion Formula for Fractional Derivatives and its Application

Atanackovic, T., Stankovic, B. (2004)

Fractional Calculus and Applied Analysis

An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type.

An operational Haar wavelet method for solving fractional Volterra integral equations

Habibollah Saeedi, Nasibeh Mollahasani, Mahmoud Mohseni Moghadam, Gennady N. Chuev (2011)

International Journal of Applied Mathematics and Computer Science

A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.

Análisis de las singularidades de una ecuación diferencial fraccionaria no lineal.

Luis Vázquez (2005)

RACSAM

Se exponen las estimaciones numéricas preliminares de las singularidades de una ecuación diferencial fraccionaria no lineal. Dicha ecuación aparece en el estudio de las ondas viajeras asociadas a una ecuación de ondas que es una interpolación entre la ecuación de ondas clásica y la ecuación de Benjamin-Ono.

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Ferreira, N., Duarte, Fernando, Lima, Miguel, Marcos, Maria, Machado, J. (2008)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. This article illustrates several applications of fractional calculus in robot manipulator path planning and control....

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