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The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana–Baleanu fractional derivative. Since the new Atangana–Baleanu fractional derivative is non-singular and non-local,… Click to show full abstract
The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana–Baleanu fractional derivative. Since the new Atangana–Baleanu fractional derivative is non-singular and non-local, the Euler–Lagrange equations are proposed for the problems of Herglotz. Fractional variational Herglotz problems of variable order are considered and two cases are shown. The Noether-type theorem with this new fractional derivative is proved. Several typical examples of the results of this paper are expressed in this paper.
Journal Title: Journal of Inequalities and Applications
Year Published: 2018
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