On hybrid Caputo fractional integro-differential inclusions with nonlocal conditions
-
1834
Downloads
-
2909
Views
Authors
Bashir Ahmad
- Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Sotiris K. Ntouyas
- Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
- Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece.
Jessada Tariboon
- Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand.
Abstract
We investigate the existence of solutions for a nonlocal hybrid boundary value problem of Caputo fractional integro-differential inclusions. A hybrid fixed point theorem of Schaefer type for a sum of three
operators due to Dhage is applied to obtain the main result. The paper concludes with an illustrative
example.
Share and Cite
ISRP Style
Bashir Ahmad, Sotiris K. Ntouyas, Jessada Tariboon, On hybrid Caputo fractional integro-differential inclusions with nonlocal conditions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4235--4246
AMA Style
Ahmad Bashir, Ntouyas Sotiris K., Tariboon Jessada, On hybrid Caputo fractional integro-differential inclusions with nonlocal conditions. J. Nonlinear Sci. Appl. (2016); 9(6):4235--4246
Chicago/Turabian Style
Ahmad, Bashir, Ntouyas, Sotiris K., Tariboon, Jessada. "On hybrid Caputo fractional integro-differential inclusions with nonlocal conditions." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4235--4246
Keywords
- Caputo fractional derivative
- integro-differential inclusion
- hybrid boundary value problem
- fixed point theorem.
MSC
References
-
[1]
B. Ahmad, Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations , Appl. Math. Lett., 23 (2010), 390-394.
-
[2]
B. Ahmad, 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 (2011), 15 pages.
-
[3]
B. Ahmad, S. K. Ntouyas, An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions, Abstr. Appl. Anal., 2014 (2014), 7 pages.
-
[4]
B. Ahmad, S. K. Ntouyas , Nonlocal fractional boundary value problems with slit-strips boundary conditions , Fract. Calc. Appl. Anal., 18 (2015), 261-280.
-
[5]
B. Ahmad, S. K. Ntouyas, A. Alsaedi, Existence results for a system of coupled hybrid fractional differential equations, Sci. World J., 2014 (2014), 6 pages.
-
[6]
B. Ahmad, S. K. Ntouyas, J. Tariboon , Nonlocal hybrid boundary value problems of Caputo fractional integro- differential equations, Acta Math. Sci., 36, (2016)
-
[7]
R. P. Agarwal, D. O'Regan, S. Stanek, Positive solutions for mixed problems of singular fractional differential equations , Math. Nachr., 285 (2012), 27-41.
-
[8]
Z. Bai, W. Sun , Existence and multiplicity of positive solutions for singular fractional boundary value problems, Comput. Math. Appl., 63 (2012), 1369-1381.
-
[9]
K. Deimling, Multivalued Differential Equations, de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter & Co., Berlin (1992)
-
[10]
B. Dhage , On solvability of operator inclusions \(x \in AxBx + Cx\) in Banach algebras and differential inclusions, Commun. Appl. Anal., 14 (2010), 567-596.
-
[11]
B. C. Dhage, S. K. Ntouyas, Existence results for boundary value problems for fractional hybrid differential inclusions, Topol. Methods Nonlinar Anal., 44 (2014), 229-238.
-
[12]
B. Dhage, D. O'Regan, A fixed point theorem in Banach algebras with applications to functional integral equations, Funct. Differ. Equ., 44 (2004), 259-267.
-
[13]
Y. Ding, Z. Wei, J. Xu, D. O'Regan, Extremal solutions for nonlinear fractional boundary value problems with p-Laplacian, J. Comput. Appl. Math., 288 (2015), 151-158.
-
[14]
J. R. Graef, L. Kong, Existence of positive solutions to a higher order singular boundary value problem with fractional Q-derivatives , Fract. Calc. Appl. Anal., 16 (2013), 695-708.
-
[15]
J. Henderson, R. Luca, A. Tudorache, On a system of fractional differential equations with coupled integral boundary conditions, Fract. Calc. Appl. Anal., 18 (2015), 361-386.
-
[16]
S. Hu, N. Papageorgiou , Handbook of Multivalued Analysis, Theory I, Kluwer Academic Publishers, Dordrecht (1997)
-
[17]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo , Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
-
[18]
A. Lasota, 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.
-
[19]
S. Liang, J. Zhang , Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval, Math. Comput. Modelling, 54 (2011), 1334-1346.
-
[20]
D. O'Regan, S. Stanek, Fractional boundary value problems with singularities in space variables, Nonlinear Dynam., 71 (2013), 641-652.
-
[21]
I. Podlubny, Fractional differential equations, Mathematics in Science and Engineering, Academic Press, Inc., San Diego, CA (1999)
-
[22]
J. Sabatier, O. P. Agrawal, J. A. T. Machado (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht (2007)
-
[23]
S. Sun, Y. Zhao, Z. Han, Y. Li , The existence of solutions for boundary value problem of fractional hybrid differential equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 4961-4967.
-
[24]
J. Tariboon, S. K. Ntouyas, W. Sudsutad , Fractional integral problems for fractional differential equations via Caputo derivative, Adv. Difference Equ., 2014 (2014), 17 pages.
-
[25]
P. Thiramanus, S. K. Ntouyas, J. Tariboon, Existence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions, Abstr. Appl. Anal., 2014 (2014), 9 pages.
-
[26]
L. Zhang, B. Ahmad, G. Wang , Successive iterations for positive extremal solutions of nonlinear fractional differential equations on a half line, Bull. Aust. Math. Soc., 91 (2015), 116-128.
-
[27]
Y. Zhao, S. Sun, Z. Han, Q. Li , Theory of fractional hybrid differential equations, Comput. Math. Appl., 62 (2011), 1312-1324.