We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as ...

This paper deals with two types of systems second-order differential equations parameters: coupled the boundary conditions Sturm–Liouville type and classical Dirichlet conditions. We discuss an Ambosetti–Prodi alternative for each system. For first system, we present sufficient existence non-existence its solutions, second a multiplicity solutions. Our arguments apply lower upper solutions meth...

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 discuss integral estimates for domain of solutions to some canonical Riccati and Sturm–Liouville equations on the line. The approach is applied to Hardy and Poincaré type inequalities with weights.

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.

We prove several Liouville-type non-existence theorems for conformal mappings of complete Riemannian manifolds. As well, we provide applications of these results to General Relativity and to the theory of conharmonic transformations. M.S.C. 2010: 53C20.

The aim of the present paper is to study asymptotic properties solutions linear fractional system with Riemann–Liouville-type derivatives and distributed delays. We prove under natural assumptions (similar those used in case when are first (integer) order) existence uniqueness initial problem for these systems discontinuous functions. As a consequence, we also unique fundamental matrix homogene...

The Yamabe problem concerns finding a conformal metric on a given closed Riemannian manifold so that it has constant scalar curvature. This paper concerns mainly a fully nonlinear version of the Yamabe problem and the corresponding Liouville type problem.

The family of Liouville copulas is defined as the survival copulas of multivariate Liouville distributions, and it covers the Archimedean copulas constructed by Williamson’s d-transform. Liouville copulas provide a very wide range of dependence ranging from positive to negative dependence in the upper tails, and they can be useful in modeling tail risks. In this article, we study the upper tail...

In this paper, we consider two new uniqueness results for fuzzy fractional differential equations (FFDEs) involving Riemann-Liouville generalized H-differentiability with the Nagumo-type condition and the Krasnoselskii-Krein-type condition. To this purpose, the equivalent integral forms of FFDEs are determined and then these are used to study the convergence of the Picard successive approximati...