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چکیده
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Since there are certain challenges to solving two-dimensional fractional optimal control problems (2D-FOCPs) using analytical approaches, finding numerical ways to estimate their solution is an important topic. This article provides a new method to solve a class of these problems. Generalized fractional Vieta-Fibonacci wavelets (GFV-FWs) are first introduced in this paper, and it seems to be effective in optimising the performance index function. Our approach is based on approximating the highest fractional derivative of the state function in the ratio of time and space with GFV-FWs. Applying the Laplace transform, we propose the Riemann-Liouville fractional integral operator of the GFV-FWs. To approximate the double integral of the performance index function, we use the two-dimensional Gauss-Legendre rules (GL). The problem of two-dimensional nonlinear optimisation becomes simple to a system of algebraic equations, which is solved by Newton’s iterative method. The convergence analysis of the suggested method carried out. In conclusion, by two applied examples, we confirm the validity and feasibility of the proposed method.
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