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Optimality conditions involving the Mittag–Leffler tempered fractional derivative

  • * Corresponding author: Ricardo Almeida

    * Corresponding author: Ricardo Almeida 

R. Almeida is supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UIDB/04106/2020. M. L. Morgado acknowledges the financial support of the Portuguese FCT - Fundação para a Ciência e a Tecnologia, through projects UIDB/04621/2020 and UIDP/04621/2020

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  • In this work we study problems of the calculus of the variations, where the differential operator is a generalization of the tempered fractional derivative. Different types of necessary conditions required to determine the optimal curves are proved. Problems with additional constraints are also studied. A numerical method is presented, based on discretization of the variational problem. Through several examples, we show the efficiency of the method.

    Mathematics Subject Classification: Primary: 26A33, 49K05; Secondary: 49M05.


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  • Table 1.  Maximum of the committed absolute error in the approximation of the solution

    $ N $ 5 10 20 40
    $ E $ 8.81 $ \times 10^{-3} $ 3.61 $ \times 10^{-3} $ 1.40 $ \times 10^{-3} $ 5.24 $ \times 10^{-4} $
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