Results 51 to 60 of about 211 (181)

Isospectral integrability analysis of dynamical systems on discrete manifolds [PDF]

Opuscula Mathematica, 2012
It is shown how functional-analytic gradient-holonomic structures can be used for an isospectral integrability analysis of nonlinear dynamical systems on discrete manifolds. The approach developed is applied to obtain detailed proofs of the integrability
Denis Blackmore, Anatoliy K. Prykarpatsky, Yarema A. Prykarpatsky   +2 more
doaj   +1 more source

Compactness of Riemann–Liouville fractional integral operators

Electronic Journal of Qualitative Theory of Differential Equations, 2020
Summary: We obtain results on compactness of two linear Hammerstein integral operators with singularities, and apply the results to give new proof that Riemann-Liouville fractional integral operators of order \(\alpha\in (0,1)\) map \(L^{p}(0,1)\) to \(C[0,1]\) and are compact for each \(p\in \bigl(\frac{1}{1-\alpha},\infty\bigr]\).
openaire   +3 more sources

Fractional Integral Inequalities of Riemann–Liouville Type for Higher‐Order Differentiable Convex Mappings

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we investigate several Riemann–Liouville fractional integral inequalities for higher‐order differentiable functions using a simple and novel approach. First, we present an inequality involving fractional integrals that generalizes the right‐hand side of the fundamental Hermite–Hadamard inequality to higher‐order derivatives ...
Samet Erden, Hüseyin Budak
wiley   +1 more source

New soliton, kink and periodic solutions for fractional space–time coupled Schrödinger equation

Alexandria Engineering Journal
This work investigates the time–space fractional coupled nonlinear Schrödinger equation. By applying an appropriate wave transformation, this equation is converted into a fourth-order system of ordinary differential equations, equivalent to a Hamiltonian
Manal Alharbi, Adel Elmandouh, Mamdouh Elbrolosy   +2 more
doaj   +1 more source

Modular integrals in minimal super Liouville gravity [PDF]

Theoretical and Mathematical Physics, 2009
20 pages, 2 ...
openaire   +3 more sources

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space

Abstract and Applied Analysis, 2014
We consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and ...
Linfen Cao, Zhaohui Dai
doaj   +1 more source

A Numerical Method Combining Cubic Interpolated Propagation and Shifted Grünwald–Letnikov for Fractional Advection–Dispersion Equations

International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.
ABSTRACT Recent advances in the numerical solution of fractional partial differential equations have yielded promising results. In particular, the Shifted Grünwald–Letnikov (SGL) approach allows for a generalization of the traditional finite difference method to the context of fractional differential equations.
Pedro Victor Serra Mascarenhas, André Luís Brasil Cavalcante   +1 more
wiley   +1 more source

Capturing Complex Rate‐Dependent Behaviors of Saturated Clays: A Fractional Consistency Kinematic Hardening Viscoplastic Approach

International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.
ABSTRACT Saturated high plasticity clays show complex nonlinear, rate‐dependent, and hysteresis behaviors under non‐monotonic stress paths, requiring advanced mathematical constitutive equations for accurate description. Taking into account the inherent advantages of kinematic hardening mechanisms in simulating complex stress histories, this paper ...
Wei Cheng, Zhen‐Yu Yin
wiley   +1 more source

Liouville integrability: An effective Morales–Ramis–Simó theorem

Journal of Symbolic Computation, 2016
Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the integral curve in reduced form provided that the previous one is in reduced form with an abelian Lie algebra.
Aparicio-Monforte, A., Dreyfus, Thomas, Weil, Jacques-Arthur   +2 more
openaire   +4 more sources