On some new systems of N-ary integral equations

This chapter discusses systems of dual integral equations with generalized Legen-dre functions, Fox’s H-functions, generalized Watson functions, and with Whittaker’s functions. These systems are solved by different methods. In particular, the system of dual integral equations with Whittaker functions W_{k, it} using Weyl fractional integral and generalized Kontorovich-Lebedev transform is reduced to the system of linear equation for the unknown functions. Systems of dual integral equations are found often in the solving of a wide class of mixed boundary value problems in mathematical physics and elasticity. Such systems of integral equations have been investigated in detail. At the same time systems of dual integral equations with more complicated functions have not been investigated and therefore are interesting for study.