Solution of one hypersingular integro-differential equation defined by determinants

The paper provides an exact analytical solution to a hypersingular inregro-differential equation of arbitrary order. is defined on closed curve in the complex plane. A characteristic feature that if written using determinants. From view traditional classification equations, it should be classified as linear equations with vatiable coefficients special form. method continuation id applied. reduced boundary value problem conjugation for analytic functions some additional conditions. If this solvable, required solve two more differential class functions. conditions solvability are indicated explicitly. When these met, can also An example given.