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A spectral framework for the solution of fractional optimal control and variational problems involving Mittag–Leffler nonsingular kernel

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Abstract

A new fractional-order Dickson functions are introduced for solving numerically fractional optimal control and variational problems involving Mittag–Leffler nonsingular kernel. The type of fractional derivative in the proposed problems is the Atangana–Baleanu–Caputo fractional derivative. In the process of the method, we use fractional-order Dickson functions and their properties to provide an accurate computational technique for calculating operational matrices, at first. Then, with the help of operational matrices and the Lagrange multiplier method, these problems are reduced to a system of algebraic equations. At last, to demonstrate the effectiveness of the new method, we enforce the proposed algorithm for several examples.

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... It is worth noting that many papers have been published in this research area, which for more information can be referred to [21][22][23][24][25][26][27][28]. ...
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Pseudo-operational matrix method for the solution of variable-order fractional partial integro-differential equations
  • H Dehestani
  • Y Ordokhani
  • M Razzaghi
Dehestani H, Ordokhani Y, Razzaghi M (2020c) Pseudooperational matrix method for the solution of variable-order fractional partial integro-differential equations. Engineering with Computers. DOI: 10.1007/s00366-019-00912-z.