Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time ...

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 ...

Integral and integro-differential equations are one of the most useful mathematical tools in both pure and applied mathematics. In this article, we present a variational iteration method for solving Fredholm integro-differential equations. This study provides an analytical approximation to determine the behavior of the solution. To show the efficiency of the present method for our proble...

We detail, derive and correct the technical use of the solid angle variable identified in formal guidance that relates skyshine calculations to dose-equivalent rate. We further recommend it for use with all National Council on Radiation Protection and Measurements (NCRP), Institute of Physics and Engineering in Medicine (IPEM) and similar reports documented. In general, for beams of identical w...

In this paper the exact analytical solution is found for the BFKL Pomeron calculus in QCD , in which all Pomeron loops have been included. This solution manifests the geometrical scaling behaviour and matches with the solution to the linear evolution equation on the line r2 = 1/Qs(x) where r is the dipole size and Qs is the saturation momentum.

some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of G...

In the context of the braneworld, a spherically symmetric, static and nonhomogeneous stellar distribution with local and non-local bulk terms is studied. Using a toy solution, it is shown how the general relativistic limit could be lost while a solution is being generated on the brane. The source of this problem is clearly identified and solved by a general solution where a constraint can be id...

Different analytical approximations to the time-dependent fission-decay width used to extract the influence of dissipation on the fission process are critically examined. Calculations with a new, highly realistic analytical approximation to the exact solution of the Fokker-Planck equation sheds doubts on previous conclusions on the dissipation strength made on the basis of less realistic approx...