This paper aims to study the q-wavelet and the q-wavelet transforms, associated with the q-Bessel operator for a fix q ∈]0, 1[. As application, an inversion formulas of the q-Riemann-Liouville and q-Weyl transforms using q-wavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.

We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann–Liouville approach. A necessary optimality condition of Euler–Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. M.S.C. 2010: 49K21, 35R11.

In this paper, we shall discuss the properties of the well-known Mittag–Leffler function, and consider the existence of solution of the periodic boundary value problem for a fractional differential equation involving a Riemann–Liouville sequential fractional derivative by means of the method of upper and lower solutions and Schauder fixed point theorem.

We determine eigenvalue intervals of λ1 and λ2 for the existence of at least one positive solution for a coupled system of Riemann–Liouville type multi-point fractional order boundary value problems by utilizing a fixed point theorem on a cone under suitable conditions.

A Riemannian manifold resp. a complex space X is called Liouville if it carries no nonconstant bounded harmonic resp. holomorphic functions. It is called Carathéodory, or Carathéodory hyperbolic, if bounded harmonic resp. holomorphic functions separate the points of X . The problems which we discuss in this paper arise from the following question: When a Galois covering X with Galois group G ov...

The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C)-valued monodromy on Riemann surfaces of genus zero with n punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at c = 1. This implies a similar representation for the isomonodromic tau-function. In the case n = 4 we thereby g...

We investigate the existence of positive solutions a Riemann-Liouville fractional differential equation with sequential derivatives, parameter and nonnegative singular nonlinearity, supplemented integral-multipoint boundary conditions which contain derivatives various orders Riemann-Stieltjes integrals. Our general cover some symmetry cases for unknown function. In proof our main result, we use...

We continue the study of quantum Liouville theory through Polyakov’s functional integral [1, 2], started in [3]. We derive the perturbation expansion for Schwinger’s generating functional for connected multi-point correlation functions involving stress-energy tensor, give the “dynamical” proof of the Virasoro symmetry of the theory and compute the value of the central charge, confirming previou...

We study the existence of positive solutions for a Riemann–Liouville fractional differential equation with sequential derivatives, parameter and sign-changing singular nonlinearity, subject to nonlocal boundary conditions containing varied derivatives general Riemann–Stieltjes integrals. also present associated Green functions some their properties. In proof main results, we apply Guo–Krasnosel...

The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, much progress has been recently achieved in both directions. objective this paper is to explore a different route, namely, construction explicit asymptotic approximations for solutions. As study case, we consider problem with left right Riemann-Liouville derivative...