The work is devoted to the proof of the uniqueness and existence of solution to local and nonlocal problems with an integral gluing condition for a loaded parabolic-hyperbolic type equation with differential and integral operators of fractional order, in which the trace of the solution appears in the Erdelyi–Kober integral operator. Using the method of energy integrals, the uniqueness of the solution is proved, and the existence of the solution is proved by the method of integral equations.

中文翻译：

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带分数阶Caputo和Erdelyi-Kober算符的抛物线-双曲型方程的Gellerstedt型问题

这项工作致力于证明局部和非局部问题解的唯一性和存在性，其中带分数阶微分和积分算子的抛物线-双曲线型方程的积分粘合条件具有积分粘连条件，其中解的轨迹出现在Erdelyi–Kober积分算子。用能量积分法证明了解的唯一性，并用积分方程法证明了解的存在性。