Inverse Problem for a Linear Equation with the Quadrat of Gerasimov–Caputo Fractional Analogue of the Pseudoparabolic Operator and Degeneration

In this article, in rectangle domain a linear boundary value problem for a Gerasimov–Caputo type fractional partial differential equation with fractional analog of the pseudoparabolic operator and degeneration is considered in the case of $$\alpha$$ -order, $$0<\alpha\leq 1$$ . The Fourier series method is used and by the Kilbas–Saigo function is obtained a countable system of ordinary differential equations. In proof of one valued solvability the method of successive approximations in combination with the method of compressing mapping is applied. Using the Cauchy–Schwarz inequality and the Bessel inequality, is proved the absolute and uniform convergence of the obtained Fourier series.