## Journal of Applied Mathematics

### Boundary Value Problems for Fractional Differential Equations with Fractional Multiterm Integral Conditions

#### Abstract

We discuss the existence and uniqueness of solutions for boundary value problems involving multiterm fractional integral boundary conditions. Our study relies on standard fixed point theorems. Illustrative examples are also presented.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 806156, 10 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305752

Digital Object Identifier
doi:10.1155/2014/806156

Mathematical Reviews number (MathSciNet)
MR3212515

#### Citation

Tariboon, Jessada; Ntouyas, Sotiris K.; Singubol, Arisa. Boundary Value Problems for Fractional Differential Equations with Fractional Multiterm Integral Conditions. J. Appl. Math. 2014 (2014), Article ID 806156, 10 pages. doi:10.1155/2014/806156. https://projecteuclid.org/euclid.jam/1425305752

#### References

• S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science, Yverdon, Switzerland, 1993.
• I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
• A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
• 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, The Netherlands, 2007.
• V. Lakshmikantham, S. Leela, and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Academic, Cambridge, UK, 2009.
• B. Ahmad and S. K. Ntouyas, “Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions,” Electronic Journal of Differential Equations, vol. 2012, no. 98, pp. 1–22, 2012.
• N. Nyamoradi and M. Javidi, “Existence of multiple positive solutions for fractional differential inclusions with $m$-point boundary conditions and two fractional orders,” Electronic Journal of Differential Equations, vol. 2012, no. 187, pp. 1–26, 2012.
• B. Ahmad and J. J. Nieto, “Sequential fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3046–3052, 2012.
• M. R. Ubriaco, “Entropies based on fractional calculus,” Physics Letters A, vol. 373, no. 30, pp. 2516–2519, 2009.
• S. Hamani, M. Benchohra, and J. R. Graef, “Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions,” Electronic Journal of Differential Equations, vol. 2010, no. 20, pp. 1–16, 2010.
• W. Sudsutad and J. Tariboon, “Existence results of fractional integro-differential equations with $m$-point multi-term fractional order integral boundary conditions,” Boundary Value Problems, vol. 2012, article 94, 11 pages, 2012.
• W. Sudsutad and J. Tariboon, “Boundary value problems for fractional differential equations with three-point fractional integral boundary conditions,” Advances in Difference Equations, vol. 2012, article 93, 10 pages, 2012.
• S. 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, vol. 33, no. 1, pp. 17–39, 2013.
• S. K. Ntouyas, “Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions,” Opuscula Mathematica, vol. 33, no. 1, pp. 117–138, 2013.
• A. Guezane-Lakoud and R. Khaldi, “Solvability of a fractional boundary value problem with fractional integral condition,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 4, pp. 2692–2700, 2012.
• B. Ahmad, S. K. Ntouyas, and A. Assolami, “Caputo type fractional differential equations with nonlocal Riemann-Liouville integral boundary conditions,” Journal of Applied Mathematics and Computing, vol. 41, no. 1-2, pp. 339–350, 2013.
• M. A. Krasnosel'skiĭ, “Two remarks on the method of successive approximations,” Uspekhi Matematicheskikh Nauk, vol. 10, no. 1(63), pp. 123–127, 1955.
• A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2003. \endinput