# Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)

- Volume: 33, Issue: 1, page 17-39
- ISSN: 1509-9407

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topSotiris K. Ntouyas. "Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 33.1 (2013): 17-39. <http://eudml.org/doc/270283>.

@article{SotirisK2013,

abstract = {This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.},

author = {Sotiris K. Ntouyas},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {fractional differential equations; fractional differential inclusions; nonlocal boundary conditions; fixed point theorems; Leray-Schauder degree},

language = {eng},

number = {1},

pages = {17-39},

title = {Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions},

url = {http://eudml.org/doc/270283},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Sotiris K. Ntouyas

TI - Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2013

VL - 33

IS - 1

SP - 17

EP - 39

AB - This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.

LA - eng

KW - fractional differential equations; fractional differential inclusions; nonlocal boundary conditions; fixed point theorems; Leray-Schauder degree

UR - http://eudml.org/doc/270283

ER -

## References

top- [1] R.P. Agarwal, B. Andrade and C. Cuevas, Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations, Nonlinear Anal. Real World Appl. 11 (2010) 3532-3554. doi: 10.1016/j.nonrwa.2010.01.002 Zbl1248.34004
- [2] 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
- [3] B. Ahmad, T. Hayat and S. Asghar, Diffraction of a plane wave by an elastic knife-edge adjacent to a strip, Canad. Appl. Math. Quart. 9 (2001) 303-316. Zbl1049.76059
- [4] B. Ahmad and S.K. Ntouyas, Existence results for nonlinear fractional differential equations with four-point nonlocal type integral boundary conditions, Afr. Diaspora J. Math. 11 (2011) 29-39. Zbl1241.26004
- [5] B. Ahmad and S.K. Ntouyas, Some existence results for boundary value problems for fractional differential inclusions with non-separated boundary conditions, Electron. J. Qual. Theory Differ. Equ. 71 (2010) 1-17. doi: 10.1155/2010/279493 Zbl1206.26005
- [6] B. Ahmad and S. Sivasundaram, On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order, Appl. Math. Comput. 217 (2010) 480-487. doi: 10.1016/j.amc.2010.05.080
- [7] B. Ahmad, Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations, Appl. Math. Lett. 23 (2010) 390-394. doi: 10.1016/j.aml.2009.11.004
- [8] B. Ahmad and J.J. Nieto, Existence of solutions for nonlocal boundary value problems of higher order nonlinear fractional differential equations, Abstr. Appl. Anal., (2009), Article ID 494720, 9 pages. Zbl1186.34009
- [9] 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
- [10] B. Ahmad and J.J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl. 58 (2009) 1838-1843. doi: 10.1016/j.camwa.2009.07.091 Zbl1205.34003
- [11] B. Ahmad, S.K. Ntouyas and A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions, Adv. Differ. Equ., Volume 2011, Article ID 107384, 11 pages. Zbl1204.34005
- [12] S. Asghar, B. Ahmad and M. Ayub, Diffraction from an absorbing half plane due to a finite cylindrical source, Acustica-Acta Acustica 82 (1996) 365-367. Zbl0887.76066
- [13] Z.B. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal. 72 (2010) 916-924. doi: 10.1016/j.na.2009.07.033 Zbl1187.34026
- [14] K. Balachandran and J. J. Trujillo, The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear Anal. 72 (2010) 4587-4593. doi: 10.1016/j.na.2010.02.035 Zbl1196.34007
- [15] D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo, Fractional calculus models and numerical methods. Series on Complexity, Nonlinearity and Chaos (World Scientific, Boston, 2012). Zbl1248.26011
- [16] D. Baleanu and O.G. Mustafa, On the global existence of solutions to a class of fractional differential equations, Comp. Math. Appl. 59 (2010) 1835-1841. doi: 10.1016/j.camwa.2009.08.028 Zbl1189.34006
- [17] D. Baleanu, O.G. Mustafa and D. O'Regan, A Nagumo-like uniqueness theorem for fractional differential equations, J. Phys. A, Math. Theor. 44 (39) (2011) 6 p. Article ID 392003.
- [18] 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
- [19] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988) 69-86. Zbl0677.54013
- [20] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580 (Springer-Verlag, Berlin-Heidelberg-New York, 1977). doi: 10.1007/BFb0087685
- [21] 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
- [22] K. Deimling, Multivalued Differential Equations (Walter De Gruyter, Berlin-New York, 1992). doi: 10.1515/9783110874228 Zbl0760.34002
- [23] M. Frigon, Théorèmes d'existence de solutions d'inclusions différentielles, Topological Methods in Differential Equations and Inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C, Vol. 472, Kluwer Acad. Publ. (Dordrecht, 1995) 51-87.
- [24] A. Granas and J. Dugundji, Fixed Point Theory (Springer-Verlag, New York, 2005). Zbl1025.47002
- [25] A. Guezane-Lakoud and R. Khaldi, Solvability of a fractional boundary value problem with fractional integral condition, Nonlinear Anal. 75 (2012) 2692-2700. doi: 10.1016/j.na.2011.11.014 Zbl1239.26007
- [26] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Theory I (Kluwer, Dordrecht, 1997).
- [27] 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).
- [28] M.A. Krasnoselskii, Two remarks on the method of successive approximations, Uspekhi Mat. Nauk 10 (1955) 123-127.
- [29] M. Kisielewicz, Differential Inclusions and Optimal Control (Kluwer, Dordrecht, The Netherlands, 1991).
- [30] 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. Sci. Math. Astronom. Phys. 13 (1965) 781-786. Zbl0151.10703
- [31] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
- [32] 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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