We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic e...

‎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...

This paper presents the application of Fractional Order PID controller as a supplementary controller to improve the dynamics of LFC in multi area deregulated power system. FOPID is a PID controller whose derivative and integral orders are of fractional rather than integer. The extension of derivative and integration order from integer to fractional order provides more flexibility in design of t...

Fractional Fourier Transform (FRFT) contains simultaneity the time-frequency information of the signal, and it is considered a new tool for time-frequency analysis. The energy distribution of image is analyzed and simulated in this paper, the characteristic of the amplitude and phase is extracted in Fractional Fourier domain of an image. The simulation results show that the FRFT can represent t...

We examine the stochastic parabolic integral equation of convolution type U(t) +A ∫ t 0 k1(t− s)U(s) ds = ∫ t 0 k2(t− s)G(s) dWH(s), t ≥ 0, where U(t) takes values in Lq(O;R) with O a σ-finite measure space, and q ∈ [2,∞). The linear operator A maps D(A) ⊂ Lq(O;R) into Lq(O;R), is nonnegative and admits a bounded H∞-calculus on Lq(O;R). The kernels are powers of t, with k1(t) = 1 Γ(α) t α−1, k2...

B. A. Piot,1 J. Kunc,1,2 M. Potemski,1 D. K. Maude,1 C. Betthausen,3 A. Vogl,3 D. Weiss,3 G. Karczewski,4 and T. Wojtowicz4 1Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, F-38042 Grenoble, France 2Faculty of Mathematics and Physics, Institute of Physics, 12116 Prague, Czech Republic 3Department of Physics, Regensburg University, D-93053 Regensburg, Germany 4Institute ...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

13.1 LTE Physical Layer ........................................................................ 456 13.1.1 Multiplexing Schemes ......................................................... 456 13.1.2 Frame Structure ................................................................. 457 13.1.3 Physical Resource Block ...................................................... 457 13.1.4 Reference Signal...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

In many intervention analysis applications, time series data may be expensive or otherwise difficult to collect. In this case the power function is helpful, because it can be used to determine the probability that a proposed intervention analysis application will detect a meaningful change. Assuming that an underlying autoregressive integrated moving average (ARIMA) or fractional ARIMA model is...