In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...

Off-resonant RF irradiation in tissue indirectly lowers the water signal by saturation transfer processes: on the one hand, there are selective chemical exchange saturation transfer (CEST) effects originating from exchanging endogenous protons resonating a few parts per million from water; on the other hand, there is the broad semi-solid magnetization transfer (MT) originating from immobile pro...

We consider the focusing mass-critical NLS iu t + u = −|u| 4/d u in high dimensions d ≥ 4, with initial data u(0) = u 0 having finite mass M(u 0) = ‫ޒ‬ d |u 0 (x)| 2 d x < ∞. It is well known that this problem admits unique (but not global) strong solutions in the Strichartz class C 0 t,loc L 2 x ∩ L 2 t,loc L 2d/(d−2) x , and also admits global (but not unique) weak solutions in L ∞ t L 2 x. I...

We consider the focusing mass-critical NLS iut+∆u = −|u|u in high dimensions d ≥ 4, with initial data u(0) = u0 having finite mass M(u0) = ∫ R |u0(x)| dx < ∞. It is well known that this problem admits unique (but not global) strong solutions in the Strichartz class C t,locL 2 x ∩ L 2 t,locL 2d/(d−2) x , and also admits global (but not unique) weak solutions in L∞t L 2 x. In this paper we introd...

The long-time behaviour of spectral semi-discretisations of weakly nonlinear wave equations is analysed. It is shown that the harmonic actions are approximately conserved also for the semi-discretised system. This permits to prove that the energy of the wave equation along the interpolated semi-discrete solution remains well conserved over long times and close to the Hamiltonian of the semi-dis...

We present an approach for the solution of a class of generalized semi-infinite optimization problems. Our approach uses augmented Lagrangians to transform generalized semi-infinite min-max problems into ordinary semi-infinite min-max problems, with the same set of local and global solutions as well as the same stationary points. Once the transformation is effected, the generalized semi-infinit...

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by g x, t I t 1 − R μe−μx while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discus...