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...

Let G be a simple digraph. The dicycle packing number of G, denoted νc(G), is the maximum size of a set of arc-disjoint directed cycles in G. Let G be a digraph with a nonnegative arcweight function w. A function ψ from the set C of directed cycles in G to R+ is a fractional dicycle packing of G if ∑ e∈C∈C ψ(C) ≤ w(e) for each e ∈ E(G). The fractional dicycle packing number, denoted ν c (G,w), ...

Identification of prognostic and predictive biomarkers is important for targeting treatments to patients and for the design and analysis of randomised controlled trials. Cox proportional hazards modelling is a standard method for assessing prognostic value of clinical biomarkers where time to occurrence of an event is the primary outcome of interest. An important issue in the analysis of progno...

This study aims to solve the most general form of linear mixed Volterra-Fredholm integro-differential equations multi-fractional order in Caputo sense (MV-FIFDEs), which is solved by using orthogonal generalized Bernstein’s polynomial expansion with collocation and moment discrete weighted residual method under suitable conditions; then, Clenshaw-Curtis formula applied approximate integral term...

By employing the generalized fractional differential operator, we introduce a system of fractional order derivative for a uniformly sampled polynomial signal. The calculation of the bring in signal depends on the additive combination of the weighted bring-in of N cascaded digital differentiators. The weights are imposed in a closed formula containing the Stirling numbers of the first kind. The ...

*Correspondence: [email protected] Department of Science, Huaihai Institute of Technology, Cangwu Road, Lianyungang, 222005, China Abstract We apply the Chebyshev polynomial-based differential quadrature method to the solution of a fractional-order Riccati differential equation. The fractional derivative is described in the Caputo sense. We derive and utilize explicit expressions of weighting coef...

Iteration is involved in the fields of dynamical systems and numerical computation and so forth. The computation of iteration is difficult for general functions even for some simple functions such as linear fractional functions . In this paper, we discuss fractional polynomial function and use the method of conjugate similitude to obtain its expression of general iterate of order n under two di...

Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fib...