This paper studies analytic Liouville-non-integrable and C∞-Liouvilleintegrable Hamiltonian systems with two degrees of freedom. We will show that considerably general Hamiltonians than the one studied in [2] have the property. We also show that a certain monodromy property of an ordinary differential equation obtained as a subsystem of a given Hamiltonian and the transseries expansion of a fir...

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

Timelike Liouville theory admits the sphere S as a real saddle point, about which quantum fluctuations can occur. An issue occurs when computing the expectation values of specific types of quantities, like the distance between points. The problem being that the gauge redundancy of the path integral over metrics is not completely fixed even after fixing to conformal gauge by imposing gμν = e g̃μν...

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...

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 ∆.

Inspired by Polyakov’s original formulation [1, 2] of quantum Liouville theory through functional integral, we analyze perturbation expansion around a classical solution. We show the validity of conformal Ward identities for puncture operators and prove that their conformal dimension is given by the classical expression. We also prove that total quantum correction to the central charge of Liouv...

In this paper, we studied q-analogue of Sturm–Liouville boundary value problem on a finite interval having discontinuity in an interior point. We proved that the q-Sturm–Liouville is self-adjoint modified Hilbert space. investigated spectral properties eigenvalues and eigenfunctions problem. shown are form complete system. Finally, sampling theorem for integral transforms whose kernels basic fu...

In this paper, some new estimates on Fej?r sort inequalities via Riemann Liouville fractional integral for the products of two harmonically-convex functions are obtained.

In this research, we introduce some new fractional integral inequalities of Minkowski’s type by using Riemann-Liouville operator. We replace the constants that appear on inequality two positive functions. Further, establish related to reverse Minkowski via integral. Using operator, special cases are also discussed.

In this paper the inverse eigenvalue problem of recovering the real coefficients in a Sturm–Liouville problem with nonselfadjoint boundary conditions depending on the spectral parameter from the eigenvalues is solved using entire-function theory and the solution of a Marchenko integral equation.