We consider the Euler–Darboux equation with parameters such that their absolute values are equal to $$ \frac{1}{2} . Since Cauchy problem in classical formulation is ill-posed for of parameters, we propose formulations and solutions modified Cauchy-type problems following parameters: (a) \alpha =\beta =\frac{1}{2}; (b) =-\frac{1}{2}\ \mathrm{and}\ \beta (c) =-\frac{1}{2}. In case (a), solved by...

In this article, the anti-plane deformation of an orthotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier cosine transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is em...

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

We define a new theory of discrete Riemann surfaces and present its basic results. The key idea is to consider not only a cellular decomposition of a surface, but the union with its dual. Discrete holomorphy is defined by a straightforward discretisation of the Cauchy-Riemann equation. A lot of classical results in Riemann theory have a discrete counterpart, Hodge star, harmonicity, Hodge theor...

The inverse problem of amplitude reconstruction on an inclined line based the values or its module as recorded semi-infinite orthogonal to beam propagation direction is considered within framework 2D parabolic equation. It demonstrated that this problem, in case when complex image plane known, can be reduced a singular Cauchy type integral existence solutions requires certain conditions met but...

In the three-dimensional open rectangular domain, problem of identification redefinition function for a partial differential equation with Gerasimov–Caputo-type fractional operator, degeneration, and integral form condition is considered in case 0<??1 order. A positive parameter present mixed derivatives. The solution this studied class regular functions. Fourier series method used, countabl...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...