Optimal Control Problem for a Linear Pseudoparabolic Equation with Final Condition, Degeneration and Gerasimov-Caputo Operator

In this paper, a linear mixed optimal control problem for a fractional analogue of a pseudoparabolic differential equation with final point integral condition and degeneration is considered in rectangular domain for 0 < α ≤ 1. Fractional operator is of Gerasimov-Caputo type and the differential equation involves two spatial variables.Control function has a nonlinear form and depends on time variable.The minimization of quality functional is considered.The Fourier series method is used and the necessary optimality conditions for nonlinear control are stated using the Kilbas-Saigo function.The determination of the optimal control function is reduced to the solution of a complicated functional integral equation, involving the product of two integrals.The countable system of integral equations and functional integral equations are solved by the method of successive approximations and contraction mapping.Absolute and uniform convergence of the obtained Fourier series is proved.

Hali tarjima qilinmagan