Hypersingular integro-differential equations with power factors in coefficients

Abstract

The linear hypersingular integro-differential equation of arbitrary order on a closed curve located on the complex plane is considered. A scheme is proposed to study this equation in the case when its coefficients have some particular structure. This scheme providers for the use of generalized Sokhotsky formulas, the solution of the Riemann boundary value problem and the solution in the class of analytical functions of linear differential equations. According to this scheme, the equations are explicitly solved, the coefficients of which contain power factors, so that along with the Riemann problem the arising differential equations are constructively solved. Solvability conditions, solution formulas, examples are given.

Keywords

• integro-differential equations
• hypersingular integrals
• generalized sokhotsky formulas
• riemann boundary problem
• linear differential equations