Pure Fractional Optimal Control of Partial Differential Equations: Nonlinear, Delay and Two-Dimensional PDEs

Abstract

Novel methods for solving the optimal control problems of different and new types of the fractional partial differential equations (PDEs) as: nonlinear PDEs, delay PDEs, and two-dimensional PDEs, are introduced in this paper. These problems are formulated with the constant Riemann–Liouville performance indices together with tracking, constant Riemann–Liouville performance indices in which there are additional terms for the tracking optimal control of PDEs. These pure fractional optimal control problems are transformed into quadratic programing ones and there is no need to derive any optimality conditions. Some challenging optimal control problems of PDEs that have applications in real-world systems are investigated. As an unprecedented constraint, we introduce Riemann–Liouville, two-dimensional isoperimetric constraint in the PDE optimal control problem.