The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate Times), available on the web, and apply it to the minimal time problem of...
It is based on recent theoretical developmentsof geometric optimal control, and the article contains a reviewof second order optimality conditions.The computations are related to a testof positivity of the intrinsic second order derivative or a test ofsingularity of the extremal flow. We derive an ...
Fract. Calc. Appl. Anal. 2019, 22, 245–252. [Google Scholar] [CrossRef] Abu-Shady, M.; Kaabar, M.K.A. A Generalized Definition of the Fractional Derivative with Applications. Math. Probl. Eng. 2021, 2021, 9444803. [Google Scholar] [CrossRef] Abu-Shady, M.; Kaabar, M.K.A....
A weak singularity in the solution of time-fractional differential equations can degrade the accuracy of numerical methods when employing a uniform mesh, especially with schemes involving the Caputo derivative (order α,), where time accuracy is of the o
Meanwhile, the temporal integer derivative ∂ u ∂ t at any point t n − 1 + σ ( ∀ σ ∈ [ 1 2 , 1 ] ) is approximated by some second-order σ formulas which are proposed in [21]. The second-order σ formulas are called second-order θ schemes in [21]. Some terms ...