Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the ...

In this paper we study fractional type operators with more than one kernel, defined by Tα,mf(x) = ˆRn k1(x − A1y)k2(x − A2y). . . km(x − Amy)f(y) dy, where, for 1 ≤ i ≤ m, each ki satisfies a fractional size condition and ...

This paper introduce the basic general theory for Linear Sequential Fractional Differential Equations which includes a recurrence relationship, involving the Riemann-Liouville fractional operator. The presented equation ...

We study continuity properties for commutators of Calderón-Zygmund and fractional integral operators between generalized Zygmund spaces of L log L type, in the variable exponent setting with different weights. In order to ...

We establish dynamical localization for random Dirac operators on the d-dimensional lattice, with d∈ {1 , 2 , 3 } , in the three usual regimes: large disorder, band edge and 1D. These operators are discrete versions of the ...

In this article we investigate the solution of the steady-state fractional diffusion equation on a bounded domain in R-1. The diffusion operator investigated, motivated by physical considerations, is neither the Riemann-Liouville ...

In this paper, fractional order (FO) operators and adaptive passivity-based controllers (APBC) are combined. The main aim is to explore possible advantages of combining FO operators and APBC over the use of integer order ...

Let b be a BMO function, 0 < α < 1 and I+,k α,b the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) ...

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. ...

This article deals with certain kind of potential operator defined as convolution with the generalized function Wα (P ± i0,m,n)depending on a complex parameter α and a real non negative one m. The definitory formulae ...