Boundary value problems for fractional differential equations with fractional multiterm integral conditions. (English) Zbl 1442.34026
Summary: 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.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
References:
| [1] | Samko, S. G.; Kilbas, A. A.; Marichev, O. I., Fractional Integrals and Derivatives, Theory and Applications, xxxvi+976 (1993), Yverdon, Switzerland: Gordon and Breach Science, Yverdon, Switzerland · Zbl 0818.26003 |
| [2] | Podlubny, I., Fractional Differential Equations. Fractional Differential Equations, Mathematics in Science and Engineering, 198, xxiv+340 (1999), San Diego, Calif, USA: Academic Press, San Diego, Calif, USA · Zbl 0924.34008 |
| [3] | Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations. Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, xvi+523 (2006), Amsterdam, The Netherlands: Elsevier Science B.V., Amsterdam, The Netherlands · Zbl 1092.45003 |
| [4] | Sabatier, J.; Agrawal, O. P.; Machado, J. A. T., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, xiv+552 (2007), Dordrecht, The Netherlands: Springer, Dordrecht, The Netherlands · Zbl 1116.00014 · doi:10.1007/978-1-4020-6042-7 |
| [5] | Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J., Theory of Fractional Dynamic Systems (2009), Cambridge, UK: Cambridge Academic, Cambridge, UK · Zbl 1188.37002 |
| [6] | Ahmad, B.; Ntouyas, S. K., Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions, Electronic Journal of Differential Equations, 2012, 98, 1-22 (2012) · Zbl 1253.26003 |
| [7] | Nyamoradi, N.; Javidi, M., Existence of multiple positive solutions for fractional differential inclusions with \(m\)-point boundary conditions and two fractional orders, Electronic Journal of Differential Equations, 2012, 187, 1-26 (2012) · Zbl 1328.47084 |
| [8] | Ahmad, B.; Nieto, J. J., Sequential fractional differential equations with three-point boundary conditions, Computers & Mathematics with Applications, 64, 10, 3046-3052 (2012) · Zbl 1268.34006 · doi:10.1016/j.camwa.2012.02.036 |
| [9] | Ubriaco, M. R., Entropies based on fractional calculus, Physics Letters A, 373, 30, 2516-2519 (2009) · Zbl 1231.82024 · doi:10.1016/j.physleta.2009.05.026 |
| [10] | Hamani, S.; Benchohra, M.; Graef, J. R., Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions, Electronic Journal of Differential Equations, 2010, 20, 1-16 (2010) · Zbl 1185.26010 |
| [11] | Sudsutad, W.; Tariboon, J., Existence results of fractional integro-differential equations with \(m\)-point multi-term fractional order integral boundary conditions, Boundary Value Problems, 2012, article 94 (2012) · Zbl 1278.26014 · doi:10.1186/1687-2770-2012-94 |
| [12] | Sudsutad, W.; Tariboon, J., Boundary value problems for fractional differential equations with three-point fractional integral boundary conditions, Advances in Difference Equations, 2012, article 93 (2012) · Zbl 1293.34013 · doi:10.1186/1687-1847-2012-93 |
| [13] | Ntouyas, S. K., 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, 17-39 (2013) · Zbl 1307.34016 · doi:10.7151/dmdico.1146 |
| [14] | Ntouyas, S. K., Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions, Opuscula Mathematica, 33, 1, 117-138 (2013) · Zbl 1277.34008 · doi:10.7494/OpMath.2013.33.1.117 |
| [15] | Guezane-Lakoud, A.; Khaldi, R., Solvability of a fractional boundary value problem with fractional integral condition, Nonlinear Analysis: Theory, Methods & Applications, 75, 4, 2692-2700 (2012) · Zbl 1239.26007 · doi:10.1016/j.na.2011.11.014 |
| [16] | Ahmad, B.; Ntouyas, S. K.; Assolami, A., Caputo type fractional differential equations with nonlocal Riemann-Liouville integral boundary conditions, Journal of Applied Mathematics and Computing, 41, 1-2, 339-350 (2013) · Zbl 1300.34013 · doi:10.1007/s12190-012-0610-8 |
| [17] | Krasnosel’skiĭ, M. A., Two remarks on the method of successive approximations, Uspekhi Matematicheskikh Nauk, 10, 1(63), 123-127 (1955) · Zbl 0064.12002 |
| [18] | Granas, A.; Dugundji, J., Fixed Point Theory. Fixed Point Theory, Springer Monographs in Mathematics, xvi+690 (2003), New York, NY, USA: Springer, New York, NY, USA · Zbl 1025.47002 · doi:10.1007/978-0-387-21593-8 |
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