Abstract
This article discusses the control system of fractional endpoint variable variational problems. For this problem, we prove the Euler-Lagrange type necessary conditions which must be satisfied for the given functional to be extremum. Finally, one example is provided to show the application of our results.
Highlights
Fractional calculus is an old mathematical topic since the seventeenth century, yet it has only received much attention and interest in the past years
As one of the important topics in control theory, the variational method plays an important role in the analysis control systems and is an important branch of mathematics study functional extremum
In [ ], Bhrawy et al investigated a new spectral collocation scheme, which obtained a numerical solution of this equation with variable coefficients on a semi-infinite domain
Summary
Fractional calculus is an old mathematical topic since the seventeenth century, yet it has only received much attention and interest in the past years. The numerical methods for solving fractional differential equations, optimal control and variational problems have a good development. T, x, Dαt ,tx, Dβt,tf x dt t and the boundary conditions x(t ) = x , x(tf ) = xf are fixed. In Section , we give the necessary conditions for the fractional-order functional variational problem with fixed and variable boundary.
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