Well-Posedness of Boundary-Value Problems for Conditionally Well-Posed Integro-Differential Equations and Polynomial Approximations of Their Solutions

The this paper, we introduce a pair of Sobolev spaces with special Jacobi–Gegenbauer weights, in which the general boundary-value problem for class ordinary integro-differential equations characterized by positivity difference orders inner and outer differential operators is well-posed Hadamard sense. Based on result, justify polynomial projection method solving corresponding problem. An application results to proof convergence Galerkin Cauchy weighted space given. rate terms best approximations an exact solution, automatically responds smoothness properties coefficients equation.