We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q ∈ 1, 2 based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation ...

Based on the quark propagator in the instanton dilute liquid approximation, we calculate analytically the quark condensate < q̄q >, the mixed quark gluon condensate gs < q̄Gμνσ q > and the four quark condensate < q̄Γqq̄Γq > at the mean field level in the framework of global color symmetry model. The numerical calculation shows that the values of these condensates are compatible with the ranges dete...

We study the effective approximation for a nonlocal stochastic Schrödinger equation with rapidly oscillating, periodically time-dependent potential. use natural diffusive scaling of heterogeneous system and limit behavior as parameter tends to 0. This is motivated by data assimilation non-Gaussian uncertainties. The operator in this partial differential generator Lévy-type process (i.e., class ...

We study the excitations at the edge of a two-dimensional electron droplet in a magnetic field in terms of a contour dynamics formalism. We find that, beyond the usual linear approximation, the nonlinear analysis yields soliton solutions which correspond to uniformly rotating shapes. These modes are found from a perturbative treatment of a nonlinear eigenvalue problem and as solutions to a modi...

In this paper the authors prove existence, uniqueness and approximation of the solutions for initial value problems of nonlinear fractional differential equations with nonlocal conditions, using the operator theoretic technique in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorem of Dhage (2014) in a partia...

We use the variational quantum Monte Carlo method to calculate the density-functional exchange-correlation hole n(xc), the exchange-correlation energy density e(xc), and the total exchange-correlation energy E(xc) of several strongly inhomogeneous electron gas systems. We compare our results with the local density approximation and the generalized gradient approximation. It is found that the no...