فهرست نشریات علمی دسترسی آزاد ایران

The generalized solvability of a nonlinear optimal control for thermal and diffusion processes in a mixed inverse problem for a Barenblatt-Zheltov-Kochina differential equation with Hilfer fractional operator is studied. The inverse problem is considered with spectral and intermediate conditions. Eigenvalues, eigenfunctions, and associated functions of the spectral problem are found and the corresponding adjoint problem is solved. Countable systems of fractional order differential equations with final value conditions are obtained. The necessary optimality conditions for nonlinear control are formulated. The determination of the optimal control function is reduced to solve a complicated nonlinear functional integral equation, and the process of solving consists of solving separately taken two nonlinear functional-integral equations. Nonlinear functional integral equations are solved by the method of successive approximations and the unique solvability of these equations is proved by the method of contracting mapping. Approximate calculations for the optimal control function, the redefinition function, and the state function of the controlled process are obtained. The absolute and uniform convergence of the obtained Fourier series are proved.