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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 823961, 9 pages
On a Multipoint Boundary Value Problem for a Fractional Order Differential Inclusion on an Infinite Interval
1Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149, Iran
2Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, 06530 Ankara, Turkey
3Institute of Space Sciences, P.O. BOX MG-23, 76900 Magurele, Bucharest, Romania
4Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
5Department of Mathematics, Texas A & M University-Kingsville, 700 University Boulevard, Kingsville, USA
6Department of Mathematics, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
Received 12 January 2013; Accepted 22 January 2013
Academic Editor: José Tenreiro Machado
Copyright © 2013 Nemat Nyamoradi et al. 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.
- S. Liang and J. Zhang, “Existence of multiple positive solutions for -point fractional boundary value problems on an infinite interval,” Mathematical and Computer Modelling, vol. 54, no. 5-6, pp. 1334–1346, 2011.
- A. M. A. El-Sayed, “Nonlinear functional-differential equations of arbitrary orders,” Nonlinear Analysis. Theory, Methods & Applications, vol. 33, no. 2, pp. 181–186, 1998.
- A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems. I,” Applicable Analysis, vol. 78, no. 1-2, pp. 153–192, 2001.
- A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems. II,” Applicable Analysis, vol. 81, no. 2, pp. 435–493, 2002.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific, Singapore, 2012.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- I. Podlubny, The Laplace Transform Method for Linear Differential Equations of Fractional Order, Slovac Academy of Science, Slovak Republic, 1994.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Amsterdam, The Netherlands, 1993.
- R. P. Agarwal, M. Benchohra, and S. Hamani, “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 973–1033, 2010.
- V. Lakshmikantham and A. S. Vatsala, “Basic theory of fractional differential equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 8, pp. 2677–2682, 2008.
- N. Nyamoradi, “Existence of solutions for multi point boundary value problems for fractional differential equations,” Arab Journal of Mathematical Sciences, vol. 18, no. 2, pp. 165–175, 2012.
- N. Nyamoradi, “Positive solutions for multi-point boundary value problem for nonlinear fractional differential equations,” Journal of Contemporary Mathematical Analysis. Accepted for publishing.
- N. Nyamoradi, “A Six-point nonlocal integral boundary value problem for fractional differential equations,” Indian Journal of Pure and Applied Mathematics, vol. 43, no. 5, pp. 429–454, 2012.
- N. Nyamoradi and T. Bashiri, “Multiple positive solutions for nonlinear fractional differential systems,” Fractional Differential Calculus, vol. 2, no. 2, pp. 119–128, 2012.
- N. Nyamoradi and T. Bashiri, “Existence of positive solutions for fractional differential systems with multi point boundary conditions,” Annali Dell'Universita di Ferrara, 2012.
- R. P. Agarwal and B. Ahmad, “Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1200–1214, 2011.
- B. Ahmad and S. K. Ntouyas, “Existence results for nonlocal boundary value problems of fractional differential equations and inclusions with strip conditions,” Boundary Value Problems, vol. 2012, article 55, 21 pages, 2012.
- A. M. A. El-Sayed and A.-G. Ibrahim, “Multivalued fractional differential equations,” Applied Mathematics and Computation, vol. 68, no. 1, pp. 15–25, 1995.
- B. Ahmad and S. K. Ntouyas, “Existence of solutions for fractional differential inclusions with nonlocal strip conditions,” Arab Journal of Mathematical Sciences, vol. 18, no. 2, pp. 121–134, 2012.
- M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, “Existence results for fractional functional differential inclusions with infinite delay and applications to control theory,” Fractional Calculus & Applied Analysis, vol. 11, no. 1, pp. 35–56, 2008.
- A. Cernea, “Continuous version of Filippov's theorem for fractional differential inclusions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 1, pp. 204–208, 2010.
- N. Nyamoradi and M. Javidi, “Exictence of multiple positive soulutions for fractional differential inclusion with m-point boundary conditions and two fractional orders,” Electronic Journal of Differential Equations, vol. 2012, p. 126, 2012.
- A. Ouahab, “Some results for fractional boundary value problem of differential inclusions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 11, pp. 3877–3896, 2008.
- K. Deimling, Multivalued Differential Equations, vol. 1 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, Germany, 1992.
- A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2003.
- A. Bressan and G. Colombo, “Extensions and selections of maps with decomposable values,” Studia Mathematica, vol. 90, no. 1, pp. 70–85, 1988.
- J.-P. Aubin and H. Frankowska, Set-Valued Analysis, vol. 2 of Systems & Control: Foundations & Applications, Birkhäuser, Boston, Mass, USA, 1990.
- M. Kamenskii, V. Obukhovskii, and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, vol. 7 of De Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter & Co., Berlin, Germany, 2001.
- J. Musielak, Introduction to Functional Analysis, PWN, Warsaw, Poland, 1976.
- R. P. Agarwal and D. O'Regan, Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
- Y. Liu, “Existence and unboundedness of positive solutions for singular boundary value problems on half-line,” Applied Mathematics and Computation, vol. 144, no. 2-3, pp. 543–556, 2003.
- L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, The Macmillan, New York, NY, USA, 1964.
- H. Covitz and S. B. Nadler, Jr., “Multi-valued contraction mappings in generalized metric spaces,” Israel Journal of Mathematics, vol. 8, pp. 5–11, 1970.
- C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, vol. 580 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977.