Abstract:
For mixed type equation with two perpendicular lines of degeneracy we consider the boundary-value problem with nonlocal condition, connecting with the help of generalized operators of fractional integro-differentiation the trace of the normal derivative of the unknown function on the transition line and its own trace on the control characteristics and the line of degeneracy. The author proves the unique solvability of the problem.
Keywords:mixed type equations, nonlocal problem, operator of fractional integration, operator of fractional differentiation, Cauchy problem, Gauss hypergeometric function, Fredholm's integral equation.
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