The notion of moment differentiation is extended to the set generalized multisums formal power series via an appropriate integral representation and accurate estimates derivatives. main result applied characterize multisummability solution a family singularly perturbed differential equations in complex domain, broadening widely range functional be considered practice, such as fractional equatio...

Firstly the one-dimension digital fractional order SavitzkyGolay differentiator (1-D DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order, is proposed to estimate the fractional order derivative of the noisy signal. The polynomial least square fitting technology and the Riemann-Liouville fractional order derivative definition are used to ensure rob...

Abstract: The aim of this paper is to develop a subspace method for state-space identification of continuous-time systems using fractional commensurate models. As compared to the classical state-space representation, the commensurate differentiation order must be estimated besides the state-space matrices. The latter are estimated with conventional subspace-based techniques using QR and singula...

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing ...

Fractional-order differentiation offers new degrees of freedom that simplify the design of high-performance dynamic controllers. The CRONE control system design (CSD) methodology proposes the design of robust controllers by using fractional-order operators. A software toolbox has been developed based on this methodology and is freely available for the international scientific and industrial com...

Abstract Magma differentiation in arc settings has usually been attributed to an interplay of processes (fractional crystallization, assimilation, and magma mixing). Homogeneous fractional crystallization widely used model the magmatic evolution volcanic systems due its simplicity, even though boundary layer fractionation (BLF) proposed as a preponderant process hydrous systems. Both models pro...

In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with timevarying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative o...

When the image is affected by strong noise and uneven intensity, traditional active contour models often cannot obtain accurate results. In this paper, a novel adaptive fractional differential segmentation method proposed to solve above problem. At first, in order extract more texture parts of image, an adaptively matrix constructed according gradient information varying each pixel. Then, edge-...

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...