About a problem for the degenerating mixed type equation involving Caputo and Erdelyi-Kober operators fractional order.

About a problem for the mixed type equation fractional order....

Анотація

Abstract: This research work devoted to proof an existence and uniqueness of solution of a local problem for the degenerating parabolic-hyperbolic type equation with loaded terms involving a trace of solution in Erdelyi-Kober integrals. Since, the trace of solution (i.e. u(x; 0) ) is in Erdelyi-Kober integrals and hyperbolic type equation is degenerates on the line y = 0, we used some properties and estimations of hyper-geometric functions, moreover some integral equalities on the proofing process of the uniqueness and existence of solution of the investigated problem.