×
Ahmad, Bashir; Ntouyas, Sotiris K.

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. (English) Zbl 1312.34005

Fract. Calc. Appl. Anal. 17, No. 2, 348-360 (2014).
The authors are concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach’s contraction principle. An illustrative example is also included.
Reviewer: Samir Bashir Hadid (Ajman)

Cited in 91 Documents

MSC:

34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations

Keywords:

fractional derivatives and integrals; Hadamard fractional derivative; initial value the authors problems
PDF BibTeX XML Cite
\textit{B. Ahmad} and \textit{S. K. Ntouyas}, Fract. Calc. Appl. Anal. 17, No. 2, 348--360 (2014; Zbl 1312.34005)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] R.P. Agarwal, B. Ahmad, Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions. Comput. Math. Appl. 62 (2011), 1200-1214. http://dx.doi.org/10.1016/j.camwa.2011.03.001 · Zbl 1228.34009
[2] A. Aghajani, Y. Jalilian, J.J. Trujillo, On the existence of solutions of fractional integro-differential equations. Fract. Calc. Appl. Anal. 15, No 1 (2012), 44-69; DOI: 10.2478/s13540-012-0005-4; http://link.springer.com/article/10.2478/s13540-012-0005-4. · Zbl 1279.45008
[3] B. Ahmad, 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. http://dx.doi.org/10.1016/j.camwa.2009.07.091 · Zbl 1205.34003
[4] B. Ahmad, J.J. Nieto, J. Pimentel, Some boundary value problems of fractional differential equations and inclusions. Comput. Math. Appl. 62 (2011), 1238-1250. http://dx.doi.org/10.1016/j.camwa.2011.02.035 · Zbl 1228.34011
[5] B. Ahmad, J.J. Nieto, Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative. Fract. Calc. Appl. Anal. 15, No 3 (2012), 451-462; DOI: 10.2478/s13540-012-0032-1; http://link.springer.com/article/10.2478/s13540-012-0032-1. · Zbl 1281.34005
[6] B. Ahmad, S.K. Ntouyas, Fractional differential inclusions with fractional separated boundary conditions, Fract. Calc. Appl. Anal. 15, No 3 (2012), 362-382; DOI: 10.2478/s13540-012-0027-y; http://link.springer.com/article/10.2478/s13540-012-0027-y. · Zbl 1279.34003
[7] B. Ahmad, S.K. Ntouyas, A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions. Adv. Differ. Equ. 2011 (2011), Art. ID 107384, 11 pp. · Zbl 1204.34005
[8] 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, No 22 (2011), 15 pp. · Zbl 1340.34063
[9] D. Baleanu, R.P. Agarwal, O.G. Mustafa, M. Cosulschi, Asymptotic integration of some nonlinear differential equations with fractional time derivative. J. Phys. A, Math. Theor. 44, No 5 (2011), Article ID 055203, 9 p. · Zbl 1238.26008
[10] A. Cernea, A note on the existence of solutions for some boundary value problems of fractional differential inclusions. Fract. Calc. Appl. Anal. 15, No 2 (2012), 183-193; DOI: 10.2478/s13540-012-0013-4; http://link.springer.com/article/10.2478/s13540-012-0013-4. · Zbl 1281.34019
[11] N.J. Ford, M.L. Morgado, Fractional boundary value problems: analysis and numerical methods. Fract. Calc. Appl. Anal. 14, No 4 (2011), 554-567; DOI: 10.2478/s13540-011-0034-4; http://link.springer.com/article/10.2478/s13540-011-0034-4. · Zbl 1273.65098
[12] J.R. Graef, L. Kong, Q. Kong, W. Qingkai, M. Wang, Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions. Fract. Calc. Appl. Anal. 15, No 3 (2012), 509-528; DOI: 10.2478/s13540-012-0036-x; http://link.springer.com/article/10.2478/s13540-012-0036-x. · Zbl 1279.34007
[13] A. Granas, J. Dugundji, Fixed Point Theory. Springer-Verlag, New York (2005). · Zbl 1025.47002
[14] J. Henderson, R. Luca, Positive solutions for a system of nonlocal fractional boundary value problems. Fract. Calc. Appl. Anal. 16, No 4 (2013), 985-1008; DOI: 10.2478/s13540-013-0061-4; http://link.springer.com/article/10.2478/s13540-013-0061-4. · Zbl 1312.34015
[15] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam (2006). http://dx.doi.org/10.1016/S0304-0208(06)80001-0
[16] V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge (2009). · Zbl 1188.37002
[17] J. Liang, Z. Liu, X. Wang, Solvability for a couple system of nonlinear fractional differential equations in a Banach space. Fract. Calc. Appl. Anal. 16, No 1 (2013), 51-63; DOI: 10.2478/s13540-013-0004-0; http://link.springer.com/article/10.2478/s13540-013-0004-0. · Zbl 1312.34020
[18] S.K. Ntouyas and M. Obaid, A coupled system of fractional differential equations with nonlocal integral boundary conditions. Adv. Differ. Equ. 2012 (2012), #130. http://dx.doi.org/10.1186/1687-1847-2012-130 · Zbl 1350.34010
[19] I. Podlubny, Fractional Differential Equations. Academic Press, San Diego (1999). · Zbl 0924.34008
[20] 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). · Zbl 1116.00014
[21] X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett. 22 (2009), 64-69. http://dx.doi.org/10.1016/j.aml.2008.03.001 · Zbl 1163.34321
[22] J. Sun, Y. Liu, G. Liu, Existence of solutions for fractional differential systems with anti-periodic boundary conditions. Comput. Math. Appl. 64 (2012), 1557-1566. http://dx.doi.org/10.1016/j.camwa.2011.12.083 · Zbl 1268.34157
[23] J. Wang, H. Xiang, Z. Liu, Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations. Int. J. Differ. Equ. 2010 (2010), Article ID 186928, 12 p. · Zbl 1207.34012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.