The generalized solvability of a nonlinear optimal control for a thermal and diffusion processes in 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 corre- sponding 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 unique solvability of these equations are proved by the method of contracting mapping. Approximate calculations for the optimal control function, for the redefinition function and for the state function of the controlled process, are obtained. The absolutely and uniformly convergence of the obtained Fourier series are proved.
Tursun, Y. and Ramazanova, A. (2025). Inverse optimization problem for a fractional analog of the Barenblatt–Zheltov–Kochina equation. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.62338.2740
MLA
Tursun, Y. , and Ramazanova, A. . "Inverse optimization problem for a fractional analog of the Barenblatt–Zheltov–Kochina equation", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.62338.2740
HARVARD
Tursun, Y., Ramazanova, A. (2025). 'Inverse optimization problem for a fractional analog of the Barenblatt–Zheltov–Kochina equation', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.62338.2740
CHICAGO
Y. Tursun and A. Ramazanova, "Inverse optimization problem for a fractional analog of the Barenblatt–Zheltov–Kochina equation," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.62338.2740
VANCOUVER
Tursun, Y., Ramazanova, A. Inverse optimization problem for a fractional analog of the Barenblatt–Zheltov–Kochina equation. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.62338.2740
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