# Hybrid fractional integro-differential inclusions

Sotiris K. Ntouyas; Sorasak Laoprasittichok; Jessada Tariboon

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2015)

- Volume: 35, Issue: 2, page 151-164
- ISSN: 1509-9407

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topSotiris K. Ntouyas, Sorasak Laoprasittichok, and Jessada Tariboon. "Hybrid fractional integro-differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 35.2 (2015): 151-164. <http://eudml.org/doc/276666>.

@article{SotirisK2015,

abstract = {In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.},

author = {Sotiris K. Ntouyas, Sorasak Laoprasittichok, Jessada Tariboon},

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

keywords = {fractional differential equations; hybrid differential inclusions; fixed point theorems},

language = {eng},

number = {2},

pages = {151-164},

title = {Hybrid fractional integro-differential inclusions},

url = {http://eudml.org/doc/276666},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Sotiris K. Ntouyas

AU - Sorasak Laoprasittichok

AU - Jessada Tariboon

TI - Hybrid fractional integro-differential inclusions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2015

VL - 35

IS - 2

SP - 151

EP - 164

AB - In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.

LA - eng

KW - fractional differential equations; hybrid differential inclusions; fixed point theorems

UR - http://eudml.org/doc/276666

ER -

## References

top- [1] 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).
- [2] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley and Sons, New York, 1993). Zbl0789.26002
- [3] V. Lakshmikantham, S. Leela and J. Vasundhara Devi, Theory of Fractional Dynamic Systems (Cambridge Academic Publishers, Cambridge, 2009). Zbl1188.37002
- [4] V. Lakshmikantham and A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. 69 (8) (2008), 2677-2682. doi: 10.1016/j.na.2007.08.042 Zbl1161.34001
- [5] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
- [6] J. Sabatier, O.P. Agrawal and J.A.T. Machado (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering (Springer, Dordrecht, 2007). doi: 10.1007/978-1-4020-6042-7 Zbl1116.00014
- [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 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
- [9] P. Thiramanus, S.K. Ntouyas and J. Tariboon, Existence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions, Abstr. Appl. Anal. Volume 2014, Article ID 902054, 9 pages. Zbl06581195
- [10] J. Tariboon, S.K. Ntouyas and W. Sudsutad, Fractional integral problems for fractional differential equations via Caputo derivative, Adv. Differ. Equ. 2014 (2014), 181. doi: 10.1186/1687-1847-2014-181 Zbl1307.34017
- [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. (2011), Art. ID 107384, pp. 11. Zbl1204.34005
- [12] B. Ahmad and S.K. Ntouyas, A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order, Electron. J. Qual. Theory Differ. Equ. (2011) No. 22, pp. 15. doi: 10.14232/ejqtde.2011.1.22 Zbl06528026
- [13] B. Ahmad and S. Sivasundaram, Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions, Commun. Appl. Anal. 13 (2009), 121-228. Zbl1180.34003
- [14] 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 Zbl1207.45014
- [15] B. Ahmad, S.K. Ntouyas and A. Alsaedi, Existence theorems for nonlocal multi-valued Hadamard fractional integro-differential boundary value problems, J. Ineq. Appl. 2014 (2014), 454. doi: 10.1186/1029-242X-2014-454
- [16] Y. Zhao, S. Sun, Z. Han and Q. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl. 62 (2011), 1312-1324. doi: 10.1016/j.camwa.2011.03.041 Zbl1228.45017
- [17] S. Sun, Y. Zhao, Z. Han and Y. Li, The existence of solutions for boundary value problem of fractional hybrid differential equations, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 4961-4967. doi: 10.1016/j.cnsns.2012.06.001 Zbl06160173
- [18] B. Ahmad and S.K. Ntouyas, An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions, Abstr. Appl. Anal. (2014), Art. ID 705809, 7 pages. Zbl1315.34007
- [19] B.C. Dhage and S.K. Ntouyas, Existence results for boundary value problems for fractional hybrid differential inclucions, Topol. Methods Nonlinar Anal. 44 (2014), 229-238.
- [20] B. Ahmad, S.K. Ntouyas and A. Alsaedi, Existence results for a system of coupled hybrid fractional differential equations, The Scientific World Journal, Volume 2014, Article ID 426438, 6 pages.
- [21] B. Ahmad and S.K. Ntouyas, An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions, Abstr. Appl. Anal. 2014 (2014), Article ID 705809, 7 pages. Zbl1315.34007
- [22] B.C. Dhage, A fixed point theorem in Banach algebras with applications to functional integral equations, Kyungpook Math. J. 44 (2004), 145-155.
- [23] S. Sitho, S.K. Ntouyas and J. Tariboon, Existence results for hybrid fractional integro-differential equations, Bound. Value Prob. 2015 (2015), 113. doi: 10.1186/s13661-015-0376-7 Zbl06581304
- [24] 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

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