The continuity for some multilinear operators related to certain fractional singular integral operators on Triebel-Lizorkin spaces is obtained. The operators include Calderon-Zygmund singular integral operator and fractional integral operator. 1. Introduction. Let T be a Calderon-Zygmund singular integral operator; a well-known result of Coifman et al. (see [6]) states that the commutator [b, T...

In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms. We give some HermiteHadamard type inequalities for convex, harmonically convex and p-convex functions. Some results presented in this paper for p-convex ...

Abstract: The object of this study is to develop a self-tuning fractional order proportionalintegral-derivative (SFOPID) controller for controlling the mover position of a direct drive linear voice coil motor (VCM) accurately under different operational conditions. The fractional order proportional-integral-derivative (FOPID) controller can improve the control performances of the conventional i...

In this paper we study a very general quadratic integral equation of fractional order. We show that the quadratic integral equations of fractional orders has at least one monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of a measure of noncompactness related to monotonicity, introduced by J. Banaś and L. Olszowy, a...

Keywords: Analytic semigroup Banach fixed point theorem Caputo derivative Faedo–Galerkin approximations Nonlocal conditions Neutral fractional differential equation a b s t r a c t This paper is concerned with the approximation of the solution for neutral fractional differential equation with nonlocal conditions in an arbitrary separable Hilbert space H. We study an associated integral equation...

In this paper , two classes of Gaussian Processes having locally the same fractal properties as Fractional Brownian Motion are studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. In the rst class (i.e. Filtered White Noises), a time dependency of the integrand of the classical Wiener Integral associated to the Fractional Brownian Motion is ...

Firm reputation is an intangible asset that within a resource-based view can provide a sustainable competitive advantage (Barney, 1991; Carter & Ruefli, 2006; Fombrun, 1996; Roberts & Dowling, 2002). While reputation is built over time, it is highly vulnerable to being tarnished and risks being lost in no time at all (Carter & Ruefli, 2006; Davies, Chun, Vinhas da Silva & Roper, 2003; Hall, 199...

In this article we provide integral representations for the Dirichlet beta and Riemann zeta functions, which are obtained by combining Mellin transform with the fractional Fourier transform. As an application of these integral formulas we derive tractable expansions of these L-functions in the series of Meixner-Pollaczek polynomials and rising factorials.

We introduce the fractional integral corresponding to the new concept of fractional derivative recently introduced by Caputo and Fabrizio and we study some related fractional differential equations.