About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 292860, 15 pages
http://dx.doi.org/10.1155/2011/292860
Research Article

Boundary Value Problems for 饾憺 -Difference Inclusions

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received 12 October 2010; Revised 24 January 2011; Accepted 22 February 2011

Academic Editor: Yuri V. Rogovchenko

Copyright © 2011 Bashir Ahmad and Sotiris K. Ntouyas. 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 [40 citations]

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

  • Bashir Ahmad, and Sotiris K. Ntouyas, “Fractional differential inclusions with fractional separated boundary condi tions,” Fractional Calculus and Applied Analysis, vol. 15, no. 3, pp. 362–382, 2012. View at PublisherView at Google Scholar
  • Xinguang Zhang, Lishan Liu, and Yonghong Wu, “Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 1420–1433, 2012. View at PublisherView at Google Scholar
  • Bashir Ahmad, Sotiris K Ntouyas, and Ioannis K Purnaras, “Existence results for nonlocal boundary value problems of nonlinear fractional q-difference equations Difference equations: New trends and applications in biology, medicine and biotechnology,” Advances in Difference Equations, vol. 2012, 2012. View at PublisherView at Google Scholar
  • Bashir Ahmad, Ahmed Alsaedi, and Sotiris K. Ntouyas, “A study of second-order q-difference equations with boundary conditions,” Advances in Difference Equations, pp. 1–10, 2012. View at PublisherView at Google Scholar
  • Bashir Ahmad, Juan J. Nieto, and Ahmed Alsaedi, “A nonlocal three-point inclusion problem of Langevin equation with two diff erent fractional orders,” Advances in Difference Equations, 2012. View at PublisherView at Google Scholar
  • Bashir Ahmad, and Juan J. Nieto, “On nonlocal boundary value problems of nonlinear q-difference equations,” Advances in Difference Equations, pp. 1–10, 2012. View at PublisherView at Google Scholar
  • Weerawat Sudsutad, “Boundary value problems for fractional differential equations with three-po int fractional integral boundary conditions,” Advances in Difference Equations, 2012. View at PublisherView at Google Scholar
  • Bashir Ahmad, and Ahmed Alsaedi, “Nonlinear fractional differential equations with nonlocal fractional integr o-differential boundary conditions,” Boundary Value Problems, 2012. View at PublisherView at Google Scholar
  • Bashir Ahmad, and Sotiris K. Ntouyas, “Existence results for nonlocal boundary value problems of fractional differ ential equations and inclusions with strip conditions,” Boundary Value Problems, 2012. View at PublisherView at Google Scholar
  • Weerawat Sudsutad, and Jessada Tariboon, “Existence results of fractional integro-differential equations with m-point multi-term fractional order integral boundary conditions,” Boundary Value Problems, 2012. View at PublisherView at Google Scholar
  • Guotao Wang, Bashir Ahmad, and Lihong Zhang, “A Coupled System of Nonlinear Fractional Differential Equations with Multipoint Fractional Boundary Conditions on an Unbounded Domain,” Abstract and Applied Analysis, vol. 2012, pp. 1–11, 2012. View at PublisherView at Google Scholar
  • M. D. Qassim, K. M. Furati, and N.-E. Tatar, “On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative,” Abstract and Applied Analysis, vol. 2012, pp. 1–17, 2012. View at PublisherView at Google Scholar
  • Jing Wu, and Xinguang Zhang, “Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations,” Abstract and Applied Analysis, vol. 2012, pp. 1–14, 2012. View at PublisherView at Google Scholar
  • Lihong Zhang, Bashir Ahmad, Guotao Wang, and Ravi P. Agarwal, “Nonlinear fractional integro-differential equations on unbounded domains in a Banach space,” Journal of Computational and Applied Mathematics, vol. 249, pp. 51–56, 2013. View at PublisherView at Google Scholar
  • Ahmed Alsaedi, Sotiris K. Ntouyas, and Ravi P. Agarwal, “A nonlocal multi-point multi-term fractional boundary value problem with Ri emann-Liouville type integral boundary conditions involving two indices,” Advances in Difference Equations, 2013. View at PublisherView at Google Scholar
  • Ahmed Alsaedi, Afrah Assolami, and Ravi P. Agarwal, “A new class of fractional boundary value problems,” Advances in Difference Equations, 2013. View at PublisherView at Google Scholar
  • Sotiris K. Ntouyas, “Quantum calculus on finite intervals and applications to impulsive differen ce equations,” Advances in Difference Equations, 2013. View at PublisherView at Google Scholar
  • Bashir Ahmad, and Sotiris K. Ntouyas, “Existence of Solutions for Nonlinear Fractional q-Difference Inclusions with Nonlocal Robin (Separated) Conditions,” Mediterranean Journal of Mathematics, vol. 10, no. 3, pp. 1333–1351, 2013. View at PublisherView at Google Scholar
  • Jufang Wang, “Existence of solutions for nonlinear second-order q-difference equations wi th first-order q-derivatives,” Advances in Difference Equations, 2013. View at PublisherView at Google Scholar
  • Haibo Chen, and Qiming Zhang, “Existence results for fractional q-difference equations with nonlocal q-int egral boundary conditions,” Advances in Difference Equations, 2013. View at PublisherView at Google Scholar
  • Bashir Ahmad, Sotiris K. Ntouyas, and Ahmed Alsaedi, “On fractional differential inclusions with anti-periodic type integral boun dary conditions,” Boundary Value Problems, 2013. View at PublisherView at Google Scholar
  • Andrzej Skowron, and Stanislaw Walczak, “Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type,” Abstract and Applied Analysis, 2013. View at PublisherView at Google Scholar
  • Bashir Ahmad, “Boundary Value Problems for a Class of Sequential Integrodifferential Equat ions of Fractional Order,” Journal of Function Spaces and Applications, 2013. View at PublisherView at Google Scholar
  • Sotiris K. Ntouyas, and Hamed H. Alsulami, “Existence Theory for nth Order Nonlocal Integral Boundary Value Problems an d Extension to Fractional Case,” Abstract and Applied Analysis, 2013. View at PublisherView at Google Scholar
  • Bashir Ahmad, Sotiris K. Ntouyas, and Ahmed Alsaedi, “A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions,” Mathematical Problems in Engineering, vol. 2013, pp. 1–9, 2013. View at PublisherView at Google Scholar
  • Bashir Ahmad, and Hana Al-Hutami, “A Study of Nonlinear Fractional q-Difference Equations with Nonlocal Integr al Boundary Conditions,” Abstract and Applied Analysis, 2013. View at PublisherView at Google Scholar
  • Habib Mâagli, Noureddine Mhadhebi, and Noureddine Zeddini, “Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem,” Abstract and Applied Analysis, vol. 2013, pp. 1–6, 2013. View at PublisherView at Google Scholar
  • Nittaya Pongarm, Suphawat Asawasamrit, and Jessada Tariboon, “Sequential Derivatives of Nonlinear -Difference Equations with Three-Point -Integral Boundary Conditions,” Journal of Applied Mathematics, vol. 2013, pp. 1–9, 2013. View at PublisherView at Google Scholar
  • Yulin Zhao, Guobing Ye, and Haibo Chen, “Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractional -Derivatives Equation,” Abstract and Applied Analysis, vol. 2013, pp. 1–12, 2013. View at PublisherView at Google Scholar
  • Sotiris K. Ntouyas, and Bashir Ahmad, “Existence Results for a Riemann-Liouville-Type Fractional Multivalued Probl em with Integral Boundary Conditions,” Journal of Function Spaces and Applications, 2013. View at PublisherView at Google Scholar
  • Thanin Sitthiwirattham, Jessada Tariboon, and Sotiris K. Ntouyas, “Three-Point Boundary Value Problems of Nonlinear Second-Order -Difference Equations Involving Different Numbers of,” Journal of Applied Mathematics, vol. 2013, pp. 1–12, 2013. View at PublisherView at Google Scholar
  • Lihong Zhang, Bashir Ahmad, Guotao Wang, Ravi P. Agarwal, Maryem Al-Yami, and Wafa Shammakh, “Nonlocal Integrodifferential Boundary Value Problem for Nonlinear Fractional Differential Equations on an Unbounded Domain,” Abstract and Applied Analysis, vol. 2013, pp. 1–5, 2013. View at PublisherView at Google Scholar
  • Changlong Yu, and Jufang Wang, “Positive Solutions of Nonlocal Boundary Value Problem for High-Order Nonlinear Fractional -Difference Equations,” Abstract and Applied Analysis, vol. 2013, pp. 1–9, 2013. View at PublisherView at Google Scholar
  • Bashir Ahmad, and Juan Jose Nieto, “Basic Theory of Nonlinear Third-Order q-Difference Equations and Inclusions,” Mathematical Modelling and Analysis, vol. 18, no. 1, pp. 122–135, 2013. View at PublisherView at Google Scholar
  • Jessada Tariboon, and Weerawat Sudsutad, “Existence of solutions for nonlinear second-order q-difference equations with three-point multi-term q-integral boundary conditions,” International Journal of Pure and Applied Mathematics, vol. 86, no. 4, pp. 701–720, 2013. View at PublisherView at Google Scholar
  • Sotiris K. Ntouyas, “Existence of solutions for fractional differential inclusions with four-poi nt nonlocal Riemann-Liouville type integral boundary conditions,” Filomat, vol. 27, no. 6, pp. 1027–1036, 2013. View at PublisherView at Google Scholar
  • Alberto Cabada, and Lihong Zhang, “An Integral Boundary Value Problem For Nonlinear Differential Equations Of Fractional Order On An Unbounded Domain,” Journal of Integral Equations and Applications, vol. 26, no. 1, pp. 117–129, 2014. View at PublisherView at Google Scholar
  • Sotiris K. Ntouyas, “Three-point boundary value problems for nonlinear second-order impulsive q- difference equations,” Advances in Difference Equations, 2014. View at PublisherView at Google Scholar
  • Lihong Zhang, Bashir Ahmad, and Guotao Wang, “Impulsive Antiperiodic Boundary Value Problems for Nonlinear -Difference Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–5, 2014. View at PublisherView at Google Scholar
  • Jessada Tariboon, and Sotiris K. Ntouyas, “Boundary Value Problems for First-Order Impulsive Functional -Integrodifference Equations,” Abstract and Applied Analysis, vol. 2014, pp. 1–11, 2014. View at PublisherView at Google Scholar