On a multipoint boundary value problem for a fractional order differential inclusion on an infinite interval

Advances in Mathematical Physics

Volumn , Issue , 2013, Pages

  Nyamoradi, Nemat ^a   Baleanu, Dumitru ^b,c,d   Agarwal, Ravi P ^d,e  

^a RAZI UNIVERSITY   (Iran)

^b CANKAYA UNIVERSITY   (Turkey)

^c INSTITUTE OF SPACE SCIENCES   (Romania)

^d KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^e TEXAS A AND M UNIVERSITY KINGSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84876532562     PISSN: 16879120     EISSN: 16879139     Source Type: Journal    
DOI: 10.1155/2013/823961     Document Type: Article

References (35)

1. Liang S., Zhang J., Existence of multiple positive solutions for m -point fractional boundary value problems on an infinite interval. Mathematical and Computer Modelling 2011 54 5-6 1334 1346 10.1016/j.mcm.2011.04.004 MR2812158
2. El-Sayed A. M. A., Nonlinear functional-differential equations of arbitrary orders. Nonlinear Analysis. Theory, Methods & Applications 1998 33 2 181 186 10.1016/S0362-546X(97)00525-7 MR1621105 ZBL0934.34055 (Pubitemid 128403304)
3. Kilbas A. A., Trujillo J. J., Differential equations of fractional order: methods, results and problems. I. Applicable Analysis 2001 78 1-2 153 192 10.1080/00036810108840931 MR1887959 ZBL1031.34002
4. Kilbas A. A., Trujillo J. J., Differential equations of fractional order: methods, results and problems. II. Applicable Analysis 2002 81 2 435 493 10.1080/0003681021000022032 MR1928462 ZBL1033.34007
5. Baleanu D., Diethelm K., Scalas E., Trujillo J. J., Fractional Calculus Models and Numerical Methods 2012 3 Singapore World Scientific xxiv+400 Series on Complexity, Nonlinearity and Chaos 10.1142/9789814355216 MR2894576
6. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering MR1658022
7. Podlubny I., The Laplace Transform Method for Linear Differential Equations of Fractional Order 1994 Slovak Republic Slovac Academy of Science
8. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives: Theory and Applications 1993 Amsterdam, The Netherlands Gordon and Breach xxxvi+976 MR1347689
9. Agarwal R. P., Benchohra M., Hamani S., A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Applicandae Mathematicae 2010 109 3 973 1033 10.1007/s10440-008-9356-6 MR2596185 ZBL1198.26004
10. Lakshmikantham V., Vatsala A. S., Basic theory of fractional differential equations. Nonlinear Analysis. Theory, Methods & Applications 2008 69 8 2677 2682 10.1016/j.na.2007.08.042 MR2446361 ZBL1161.34001
11. Nyamoradi N., Existence of solutions for multi point boundary value problems for fractional differential equations. Arab Journal of Mathematical Sciences 2012 18 2 165 175 10.1016/j.ajmsc.2012.01.002 MR2922677 ZBL1247.35190
12. Nyamoradi N., Positive solutions for multi-point boundary value problem for nonlinear fractional differential equations. Journal of Contemporary Mathematical Analysis. Accepted for publishing
13. Nyamoradi N., A Six-point nonlocal integral boundary value problem for fractional differential equations. Indian Journal of Pure and Applied Mathematics 2012 43 5 429 454
14. Nyamoradi N., Bashiri T., Multiple positive solutions for nonlinear fractional differential systems. Fractional Differential Calculus 2012 2 2 119 128
15. Nyamoradi N., Bashiri T., Existence of positive solutions for fractional differential systems with multi point boundary conditions. Annali Dell'Universita di Ferrara 2012 10.1007/s11565-012-0160-x
16. Agarwal R. P., Ahmad B., Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions. Computers & Mathematics with Applications 2011 62 3 1200 1214 10.1016/j.camwa.2011.03. 001 MR2824708 ZBL1228.34009
17. Ahmad B., Ntouyas S. K., Existence results for nonlocal boundary value problems of fractional differential equations and inclusions with strip conditions. Boundary Value Problems 2012 2012 article 55 21 MR2930994
18. El-Sayed A. M. A., Ibrahim A.-G., Multivalued fractional differential equations. Applied Mathematics and Computation 1995 68 1 15 25 10.1016/0096-3003(94)00080-N MR1320806
19. Ahmad B., Ntouyas S. K., Existence of solutions for fractional differential inclusions with nonlocal strip conditions. Arab Journal of Mathematical Sciences 2012 18 2 121 134 10.1016/j.ajmsc.2012.01.005 MR2922673
20. Benchohra M., Henderson J., Ntouyas S. K., Ouahab A., Existence results for fractional functional differential inclusions with infinite delay and applications to control theory. Fractional Calculus & Applied Analysis 2008 11 1 35 56 MR2379272 ZBL1149.26010
21. Cernea A., Continuous version of Filippov's theorem for fractional differential inclusions. Nonlinear Analysis. Theory, Methods & Applications 2010 72 1 204 208 10.1016/j.na.2009.06.046 MR2574932 ZBL1186.34010
22. Nyamoradi N., Javidi M., Exictence of multiple positive soulutions for fractional differential inclusion with m-point boundary conditions and two fractional orders. Electronic Journal of Differential Equations 2012 2012 126
23. Ouahab A., Some results for fractional boundary value problem of differential inclusions. Nonlinear Analysis. Theory, Methods & Applications 2008 69 11 3877 3896 10.1016/j.na.2007.10.021 MR2463341 ZBL1169.34006
24. Deimling K., Multivalued Differential Equations 1992 1 Berlin, Germany Walter de Gruyter xii+260 de Gruyter Series in Nonlinear Analysis and Applications 10.1515/9783110874228 MR1189795
25. Granas A., Dugundji J., Fixed Point Theory 2003 New York, NY, USA Springer xvi+690 Springer Monographs in Mathematics MR1987179
26. Bressan A., Colombo G., Extensions and selections of maps with decomposable values. Studia Mathematica 1988 90 1 70 85 MR947921 ZBL0677.54013
27. Aubin J.-P., Frankowska H., Set-Valued Analysis 1990 2 Boston, Mass, USA Birkhäuser xx+461 Systems & Control: Foundations & Applications MR1048347
28. Kamenskii M., Obukhovskii V., Zecca P., Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces 2001 7 Berlin, Germany Walter de Gruyter & Co. xii+231 De Gruyter Series in Nonlinear Analysis and Applications 10.1515/9783110870893 MR1831201
29. Musielak J., Introduction to Functional Analysis 1976 Warsaw, Poland PWN
30. Agarwal R. P., O'Regan D., Infinite Interval Problems for Differential, Difference and Integral Equations 2001 Dordrecht, The Netherlands Kluwer Academic Publishers x+341 10.1007/978-94-010-0718-4 MR1845855
31. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier Science xvi+523 North-Holland Mathematics Studies MR2218073
32. Liu Y., Existence and unboundedness of positive solutions for singular boundary value problems on half-line. Applied Mathematics and Computation 2003 144 2-3 543 556 10.1016/S0096-3003(02)00431-9 MR1994092 ZBL1036.34027
33. Kantorovich L. V., Akilov G. P., Functional Analysis in Normed Spaces 1964 New York, NY, USA The Macmillan xiii+771 MR0213845
34. Covitz H., Nadler, S. B. Jr., Multi-valued contraction mappings in generalized metric spaces. Israel Journal of Mathematics 1970 8 5 11 MR0263062 ZBL0192.59802
35. Castaing C., Valadier M., Convex Analysis and Measurable Multifunctions 1977 580 Berlin, Germany Springer vii+278 Lecture Notes in Mathematics MR0467310