Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of Lp-solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

中文翻译：

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Erdélyi-Kober分数积分在求解时间分数Tricomi-Keldysh型方程中的应用

摘要 本文研究了时间分数阶Tricomi-Keldysh型方程的柯西问题。基于Erdélyi-Kober分数积分算子的理论，用Mittag-Leffler函数给出了涉及超贝塞尔算子的非齐次微分方程的形式解，然后应用Gronwall型不等式考虑非线性方程。最后，我们利用Mikhlin乘子定理建立了时间分数阶Tricomi-Keldysh型方程Lp解的存在唯一性。