Problem with shift for the third-order equation with discontinuous coefficients

Abstract

The unique solvability of boundary value problem with Saigo operators for the thirdorder equation with multiple characteristics was investigated. The uniqueness theorem with constraints of inequality type on the known functions and different orders of generalized fractional integro-differentiation was proved. The existence of solution is equivalently reduced to the solvability of Fredholm integral equation of the second kind.

Keywords

• boundary value problem
• gauss hypergeometric function
• operators of fractional order
• fredholm equation