Quantum Liouville theory is annualized in terms of the infinite dimensional representations of Uqsl(2,C) with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from the finite dimensional representations of Uqsl(2,C). We furthe...

This paper is devoted to boundary-value problems for Riemann–Liouville-type fractional differential equations of variable order involving finite delays. The existence solutions first studied using a Darbo’s fixed-point theorem and the Kuratowski measure noncompactness. Secondly, Ulam–Hyers stability criteria are examined. All results in this study established with help generalized intervals pie...

At present, fractional differential is the effective mathematical approach which deals with factual problems. This projected technique employs derivatives definitions Riemann-Liouville (R-L), Grunwald-Letnikov (G-L) and caputo for denoising medical image. The presented method based on derivative in turn improves quality of input image processed integer order such as pre-processing operation, co...

The formulations of Riemann-Liouville and Caputo derivatives in the complex plane are presented. Two versions corresponding to the whole or half plane. It is shown that they can be obtained from the Grünwald-Letnikov derivative.

In this work, the authors study the existence of solutions for fractional differential inclusions in the sense of Almgren with Riemann-Liouville derivative. They also show the compactness of the solution set. A Peano type existence theorem is also proved.

We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with coupled integral boundary conditions which contain some positive constants.

In this paper, we tried to evaluate the fractional derivatives by using the Chebyshev series expansion. We discuss the indefinite quadrature rule to estimate the fractional derivatives of Riemann-Liouville type.

The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann-Liouville fractional integration operator has been obtained.

In this paper, we establish some new integral inequalities for convex functions by using the Riemann-Liouville operator of non integer order. For our results some classical integral inequalities can be deduced as some special cases.

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.