in this paper we propose a relatively new semi-analytical technique to approximate the solution ofnonlinear 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 an...

Two types of laminar flows of non-Newtonian fluids in annuli with stationary outer cylinder are analysed from the viewpoint of existence of an exact analytical or almost exact analytical (quasisimilarity) solution relating volumetric flow rate and axial pressure gradient. The exact analytical solution is derived for the Vocadlo (RobertsonStiff) fluids when flow is caused simultaneously by the i...

In this paper, Newton Harmonic Balance Method (NHBM) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. Periodic solution is analytically verified and consequently the relation between the Natural Frequency and the amplitude is obtained in an ana...

In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the parameters, and show that the numerical solution reproduces exactly the analytical solution. We also show that the generalization of the SIR model, including ...

We investigate the transmission and reflection properties at the interfaces between the lossy positive-index materials (PIM) and negative-index materials (NIM) with graded permittivity and permeability. We present an exact analytical solution to Helmholtz’ equation for the oblique incidence on profile with the graded real parts of permittivity and permeability profile changing according to a hy...

a reproducing kernel hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. in this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. the analytical solution is represented in the form of series in the reproducing kernel space. some numerical ...

In literature, it is widely accepted that the design of Class-E Power Amplifier (PA) with finite dc feed inductance requires a long iterative solution procedure. To avoid such iterative solution methods, analytical design equations should be known. The problem associated with the finite dc feed inductance Class-E PA is usually ascribed to the fact that the circuit element values are transcenden...