Keywords: Relative controllability Time delays Distributed delays Fractional derivative Mittag–Leffler function a b s t r a c t This paper is concerned with the controllability of nonlinear fractional dynamical systems with time varying multiple delays and distributed delays in control defined in finite dimensional spaces. Sufficient conditions for controllability results are obtained using the...

The denomination Fractional Order Calculus has been widely used to describe the mathematical analysis of differentiation and integration to an arbitrary non-integer order, including irrational and complex orders. First proposed around three hundred years ago, it has attracted much interest during the past three decades (Oldham & Spanier (1974), Miller & Ross (1993), Podlubni (1999)). The increa...

In this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum dynamics using a new iterative method and residual power series based Caputo operator. The equation is generalization of traditional that allows for non-integer orders differentiation. This has been used in study to model behavior particles with fractional spin. Laplace transform employed into simpler form...

To solve the issues with conventional level set segmentation algorithms, which are sensitive to initial contours and less noise-resistant, a model based on coupling of texture information structural is developed. In this model, rotation invariant mask produced by fractional-order differentiation used first describe image’s global information. Then, power function energy generalization solved ap...

Semi-differentiation, or convolution as it is sometimes known, a mathematical technique commonly used to disentangle overlapping peaks in cyclic linear sweep voltammograms. However, this often misapplied due misunderstandings of fractional calculus. Additionally, rigorous treatment and validation the theory semi-differential analysis reversible, soluble-insoluble electrochemical reactions lacki...