Оn а рrоblеm fоr thе lоаdеd miхеd tуре еquаtiоn with frасtiоnаl dеrivаtivе

An existence and an uniqueness of solution of local boundary value problem with discontinuous matching condition for the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals have been investigated in this research work. The uniqueness of solution is proved by the method of integral energy and the existence is proved by the method of integral equations.