Many problems in physics like reconstruction of the radially distributed emissivity from the line-ofsight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. The aim of this communication is to propose a new algorithm for the Abel inversion by ...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory. Park et al. [8] have considered the existence of solution of fuzzy integral equation in Banach space and Subrahmaniam and Sudarsanam [12] proved the existence of solution of fuzzy functional equations. An integral equation is called singular if either the range of integration is infinite or the kernel...

In this work we are concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation with a nonsmooth solution. We investigate the application of product integration methods and a detailed analysis of the Trapezoidal method is given. In order to improve the numerical results we consider extrapolation procedures and collocation methods based on graded meshes. Sever...

A non-linear second order ODE has some applications in engineering problems. In physics, it arises the modeling of flux a heated compressible fluid through long slender tube. this paper, we consider differential equation whose analytic solution cannot be obtained directly. Therefore, first find canonical transformations to rewrite terms variables by using Lie symmetry approach. We then reduce e...

Following earlier work by Abel and others, Kummer gave functional equations for the polylogarithm function Lim(z) up to m = 5 in 1850, but no example for larger m was known until recently. We give the first genuine 2-variable functional equation for the 7–logarithm. We investigate and relate identities for the 3-logarithm given by Goncharov and Wojtkowiak and deduce a certain family of function...