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The Scientific World Journal
Volume 2013 (2013), Article ID 915437, 11 pages
http://dx.doi.org/10.1155/2013/915437
Research Article

An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Received 27 August 2013; Accepted 19 September 2013

Academic Editors: A. Atangana, S. C. O. Noutchie, and A. Secer

Copyright © 2013 Ricardo Almeida and Delfim F. M. Torres. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [9 citations]

The following is the list of published articles that have cited the current article.

  • Jackson R. G. S. Almeida, Juliane C. Silva, Amanda L. Guimarães, Ana P. Oliveira, Grasielly R. Souza, Raimundo G. Oliveira-Júnior, Sarah R. G. Lima-Saraiva, José M. Barbosa-Filho, Raimundo Braz-Filho, Dinalva Brito Queiroz, and Marco Antônio Botelho, “ 3,6-Dimethoxy-6″,6″-Dimethyl-(7,8,2″,3″)-Chromeneflavone, a Flavonoid Isolated from Lonchocarpus Araripensis Benth. (Fabaceae), Reduces Nociceptive Behaviour in Mice ,” Phytotherapy Research, 2015. View at Publisher · View at Google Scholar
  • Dina Tavares, Ricardo Almeida, and Delfim F. M. Torres, “Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order,” Optimization, vol. 64, no. 6, pp. 1381–1391, 2015. View at Publisher · View at Google Scholar
  • Yi Zhang, and Bin Yan, “Noether’s theorem for fractional Birkhoffian systems of variable order,” Acta Mechanica, vol. 227, no. 9, pp. 2439–2449, 2016. View at Publisher · View at Google Scholar
  • Sahoo, Saha Ray, Bera, and Das, “The formation of dynamic variable order fractional differential equation,” International Journal of Modern Physics C, vol. 27, no. 7, 2016. View at Publisher · View at Google Scholar
  • Behrouz Parsa Moghaddam, and José António Tenreiro Machado, “Extended Algorithms for Approximating Variable Order Fractional Derivatives with Applications,” Journal of Scientific Computing, 2016. View at Publisher · View at Google Scholar
  • Gerardo D. Anaya-Eugenio, Isabel Rivero-Cruz, Robert Bye, Edelmira Linares, and Rachel Mata, “Antinociceptive activity of the essential oil from artemisia ludoviciana,” Journal of Ethnopharmacology, 2016. View at Publisher · View at Google Scholar
  • Behrouz Parsa Moghaddam, and José António Tenreiro Machado, “A computational approach for the solution of a class of variable-order fractional integro-differential equations with weakly singular kernels,” Fractional Calculus and Applied Analysis, vol. 20, no. 4, 2017. View at Publisher · View at Google Scholar
  • Corina Drapaca, “Fractional calculus in neuronal electromechanics,” Journal of Mechanics of Materials and Structures, vol. 12, no. 1, pp. 35–55, 2017. View at Publisher · View at Google Scholar
  • Machado, and Moghaddam, “SM-algorithms for approximating the variable-order fractional derivative of high order,” Fundamenta Informaticae, vol. 151, no. 1-4, pp. 293–311, 2017. View at Publisher · View at Google Scholar