Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2013, Article ID 128043, 15 pages
http://dx.doi.org/10.1155/2013/128043
Research Article

Fractional Sobolev Spaces via Riemann-Liouville Derivatives

Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

Received 31 July 2013; Accepted 19 October 2013

Academic Editor: Ismat Beg

Copyright © 2013 Dariusz Idczak and Stanisław Walczak. 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 [11 citations]

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

  • Gabriele Bonanno, Rosana Rodriguez-Lopez, and Stepan Tersian, “Existence of solutions to boundary value problem for impulsive fractional differential equations,” Fractional Calculus and Applied Analysis, vol. 17, no. 3, pp. 717–744, 2014. View at Publisher · View at Google Scholar
  • Massimiliano Ferrara, Giovanni Molica Bisci, and Binlin Zhang, “Existence of weak solutions for non-local fractional problems via Morse theory,” Discrete and Continuous Dynamical Systems - Series B, vol. 19, no. 8, pp. 2483–2499, 2014. View at Publisher · View at Google Scholar
  • Hua Jin, and Wenbin Liu, “Eigenvalue problem for fractional differential operator containing left and right fractional derivatives,” Advances in Difference Equations, vol. 2016, no. 1, 2016. View at Publisher · View at Google Scholar
  • Rafał Kamocki, “A new representation formula for the Hilfer fractional derivative and its application,” Journal of Computational and Applied Mathematics, 2016. View at Publisher · View at Google Scholar
  • Hai Pu, and Lili Cao, “Multiple solutions for the fractional differential equation with concave-convex nonlinearities and sign-changing weight functions,” Advances in Difference Equations, vol. 2017, no. 1, 2017. View at Publisher · View at Google Scholar
  • Dariusz Idczak, “Functions of finite fractional variation and their applications to fractional impulsive equations,” Czechoslovak Mathematical Journal, vol. 67, no. 1, pp. 171–195, 2017. View at Publisher · View at Google Scholar
  • Shengzhi Luan, Yanping Lian, Yuping Ying, Shaoqiang Tang, Gregory J. Wagner, and Wing Kam Liu, “An enriched finite element method to fractional advection–diffusion equation,” Computational Mechanics, 2017. View at Publisher · View at Google Scholar
  • Wenbin Liu, Mengqiu Wang, and Tengfei Shen, “Analysis of a class of nonlinear fractional differential models generated by impulsive effects,” Boundary Value Problems, vol. 2017, no. 1, 2017. View at Publisher · View at Google Scholar
  • Maïtine Bergounioux, Antonio Leaci, Giacomo Nardi, and Franco Tomarelli, “Fractional sobolev spaces and functions of bounded variation of one variable,” Fractional Calculus and Applied Analysis, vol. 20, no. 4, 2017. View at Publisher · View at Google Scholar
  • Juan J. Nieto, Bessem Samet, and Mohamed Jleli, “Lyapunov-type inequalities for a higher order fractional differential equation with fractional integral boundary conditions,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2017, 2017. View at Publisher · View at Google Scholar
  • Mohamed Jleli, Mokhtar Kirane, and Bessem Samet, “Hartman-Wintner-Type Inequality for a Fractional Boundary Value Problem via a Fractional Derivative with respect to Another Function,” Discrete Dynamics in Nature and Society, vol. 2017, pp. 1–8, 2017. View at Publisher · View at Google Scholar