Variable Order Mittag–Leffler Fractional Operators on Isolated Time Scales and Application to the Calculus of Variations

  • Thabet AbdeljawadEmail author
  • Raziye Mert
  • Delfim F. M. Torres
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 194)


We introduce new fractional operators of variable order in isolated time scales with Mittag–Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main results give fractional integration by parts formulas and necessary optimality conditions of Euler–Lagrange type.


Fractional calculus Atangana–Baleanu fractional derivative Fractional variational problems 



Abdeljawad is grateful to Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM), number RG-DES-2017-01-17; Torres to the support of FCT within the R&D unit CIDMA, UID/MAT/04106/2019.


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Authors and Affiliations

  1. 1.Department of Mathematics and General SciencesPrince Sultan UniversityRiyadhSaudi Arabia
  2. 2.Mechatronic Engineering DepartmentUniversity of Turkish Aeronautical AssociationAnkaraTurkey
  3. 3.Department of MathematicsCenter for Research and Development in Mathematics and Applications (CIDMA), University of AveiroAveiroPortugal

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