The Cauchy problem for a nonhomogeneous time-fractional beam vibration equation involving the Gerasimov–Caputo operator

In this paper, a nonhomogeneous initial value problem posed in a half-plane for a fourthorder differential equation involving a time-fractional derivative is investigated. The problem is divided into three parts. First, the solution of the corresponding problem with homogeneous initial conditions is obtained. Subsequently, using the obtained fundamental solution, an explicit expression for the solution of the nonhomogeneous initial value problem is derived.

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