Mathematics Subject Classification: 26A33 (main), 35A22, 78A25, 93A30
The generalization of the concept of derivative to non-integer values goes
back to the beginning of the theory of differential calculus. Nevertheless, its
application in physics and engineering remained unexplored up to the last
two decades. Recent research motivated the establishment of strategies taking advantage of the Fractional Calculus (FC) in the modeling and control
of many phenomena. In fact, many classical...
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22
The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.
Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40
Fractional 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...
A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is...
This paper presents a novel zoom transform algorithm for a more reliable frequency estimation. In fact, in many signal processing problems exact determination of the frequency of a signal is of paramount importance. Some techniques derived from the Fast Fourier Transform (FFT), just pad the signal with enough zeros in order to better sample its Discrete-Time Fourier Transform. The proposed algorithm is based on the FFT and avoids the problems observed in the standard heuristic approaches. The analytic...
We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in and prove non-existence of real hypersurfaces in with generalized Tanaka-Webster...
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