Displaying similar documents to “An operational Haar wavelet method for solving fractional Volterra integral equations”

Theorem for Series in Three-Parameter Mittag-Leffler Function

Soubhia, Ana, Camargo, Rubens, Oliveira, Edmundo, Vaz, Jayme (2010)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification 2010: 26A33, 33E12. The new result presented here is a theorem involving series in the three-parameter Mittag-Leffler function. As a by-product, we recover some known results and discuss corollaries. As an application, we obtain the solution of a fractional differential equation associated with a RLC electrical circuit in a closed form, in terms of the two-parameter Mittag-Leffler function.

Fractional positive continuous-time linear systems and their reachability

Tadeusz Kaczorek (2008)

International Journal of Applied Mathematics and Computer Science

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A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.

Numerical solutions to integral equations equivalent to differential equations with fractional time

Bartosz Bandrowski, Anna Karczewska, Piotr Rozmej (2010)

International Journal of Applied Mathematics and Computer Science

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This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.

Controllability and observability of linear discrete-time fractional-order systems

Said Guermah, Said Djennoune, Maamar Bettayeb (2008)

International Journal of Applied Mathematics and Computer Science

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In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.

On the controllability of fractional dynamical systems

Krishnan Balachandran, Jayakumar Kokila (2012)

International Journal of Applied Mathematics and Computer Science

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This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

Optimal approximation simulation and analog realization of the fundamental fractional order transfer function

Abdelbaki Djouambi, Abdelfatah Charef, Alina Voda besancon (2007)

International Journal of Applied Mathematics and Computer Science

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This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems fora given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase...

On a Differential Equation with Left and Right Fractional Derivatives

Atanackovic, Teodor, Stankovic, Bogoljub (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05 We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations...