We obtain an intertwining relation between some Riemann-Liouville operators of order α ∈ (1, 2), connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely asymmetric α−stable Lévy processes. An alternative approach based on recurrent extensions of positive self-similar Markov processes and exponential functionals of Lévy processes is also ...

We consider a singular second order differential operator ∆ defined on ]0,∞[. We give nice estimates for the kernel which intervenes in the integral transform of the eigenfunction of ∆. Using these results, we establish Hardy type inequalities for Riemann-Liouville and Weyl transforms associated with the operator ∆.

We derive a high-resolution formula for the L-quantization errors of Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for related Sobolev balls. We describe a quantization procedure which leads to asymptotically optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role.

In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liou...

The oscillation criteria for forced nonlinear fractional difference equation of the form ∆x(t) + f1(t, x(t+ α)) =v(t) + f2(t, x(t+ α)), t ∈ N0, 0 < α ≤ 1, ∆x(t)|t=0 =x0, where ∆α denotes the Riemann-Liouville like discrete fractional difference operator of order α is presented. Mathematics Subject Classification: 26A33, 39A12

In this paper a new function called as K-function, which is an extension of the generalization of the Mittag-Leffler function[10,11] and its generalized form introduced by Prabhakar[20], is introduced and studied by the author in terms of some special functions and derived the relations that exists between the Kfunction and the operators of Riemann-Liouville fractional integrals and derivatives.

We derive Euler-Lagrange type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann-Liouville derivatives of order (α, β), α > 0, β > 0, recently introduced by J. Cresson and S. Darses. Some interesting consequences are obtained and discussed. Mathematics Subject Classification 2000: 49K05, 49S05, 70H33, 26A33.

In this article, we get solutions of some integral inequalities Hermite-Hadamard type and using the approach ($\psi$,$h$)-Convex function by way Riemann-Liouville Fractional integrals Katugampola operators.

We study the existence and multiplicity of positive solutions for a system Riemann–Liouville fractional differential equations with sequential derivatives, parameters sign-changing singular nonlinearities, subject to nonlocal coupled boundary conditions which contain Riemann–Stieltjes integrals various derivatives. In proof our main results we use nonlinear alternative Leray–Schauder type Guo–K...

Department of Mathematics Imperial College 180 Queen’s Gate, London SW7 2BZ, U.K. and Department of Physics “G. Galilei” Istituto Nazionale di Fisica Nucleare University of Padova Via Marzolo, 8 35131 Padova, Italy ABSTRACT This is the first part of an investigation concerning the formulation of 2D gravity in the framework of the uniformization theory of Riemann surfaces. As a first step in thi...