Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions
Bashir Ahmad; Sotiris K. Ntouyas
Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2012)
- Volume: 32, Issue: 1, page 45-62
- ISSN: 1509-9407
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topBashir Ahmad, and Sotiris K. Ntouyas. "Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 32.1 (2012): 45-62. <http://eudml.org/doc/270768>.
@article{BashirAhmad2012,
abstract = {This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.},
author = {Bashir Ahmad, Sotiris K. Ntouyas},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {fractional differential inclusions; anti-periodic; integral boundary conditions; existence; fixed point theorems},
language = {eng},
number = {1},
pages = {45-62},
title = {Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions},
url = {http://eudml.org/doc/270768},
volume = {32},
year = {2012},
}
TY - JOUR
AU - Bashir Ahmad
AU - Sotiris K. Ntouyas
TI - Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2012
VL - 32
IS - 1
SP - 45
EP - 62
AB - This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.
LA - eng
KW - fractional differential inclusions; anti-periodic; integral boundary conditions; existence; fixed point theorems
UR - http://eudml.org/doc/270768
ER -
References
top- [1] B. Ahmad, A. Alsaedi and B. Alghamdi, Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, Nonlinear Anal. Real World Appl. 9 (2008) 1727-1740. doi: 10.1016/j.nonrwa.2007.05.005 Zbl1154.34311
- [2] B. Ahmad and J.J. Nieto, Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Bound. Value Probl. 2009, Art. ID 708576, 11 pp. Zbl1167.45003
- [3] B. Ahmad and V. Otero-Espinar, Existence of solutions for fractional differential inclusions with anti-periodic boundary conditions, Bound. Value Probl. 2009 (2009), Article ID 625347, 11 pages. Zbl1172.34004
- [4] B. Ahmad and S. Sivasundaram, Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear Anal. Hybrid Syst. 4 (2010) 134-141. doi: 10.1016/j.nahs.2009.09.002 Zbl1187.34038
- [5] B. Ahmad and J.J. Nieto, Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory, Topological Methods in Nonlinear Analysis 35 (2010) 295-304. Zbl1245.34008
- [6] B. Ahmad, S.K. Ntouyas and A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions, Adv. Difference Equ. 2011, Art. ID 107384, 11 pp. Zbl1204.34005
- [7] B. Ahmad, J. Nieto and A. Alsaedi, Existence and uniqueness of solutions for nonlinear fractional differential equations with non-separated type integral boundary conditions, Acta Math. Scientia 31B (2011) 2122-2130. doi: 10.1016/S0252-9602(11)60388-3 Zbl1265.34009
- [8] M. Benchohra, John R. Graef and S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal. 87 (2008) 851-863. Zbl1198.26008
- [9] A. Boucherif, Second-order boundary value problems with integral boundary conditions, Nonlinear Anal. 70 (2009) 364-371. doi: 10.1016/j.na.2007.12.007 Zbl1169.34310
- [10] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988) 69-86. Zbl0677.54013
- [11] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl0346.46038
- [12] H. Covitz and S.B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970) 5-11. doi: 10.1007/BF02771543 Zbl0192.59802
- [13] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003. Zbl1025.47002
- [14]S. Hamani, M. Benchohra and John R. Graef, Existence results for boundary value problems with nonlinear fractional inclusions and integral conditions, Electronic J. Differential Equations 2010 (20) (2010) 1-16. Zbl1185.26010
- [15] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
- [16] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991.
- [17] A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Math. 13 (1965) 781-786. Zbl0151.10703
- [18] X. Liu, M. Jia and B. Wu, Existence and uniqueness of solution for fractional differential equations with integral boundary conditions, E.J. Qualitative Theory of Diff. Equ. 69 (2009) 1-10. Zbl1201.34010
- [19] H.A.H. Salem, Fractional order boundary value problem with integral boundary conditions involving Pettis integral, Acta Math. Scientia 31 (2011) 661-672. doi: 10.1016/S0252-9602(11)60266-X Zbl1240.26009
- [20] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993. Zbl0818.26003
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