×
Ahmad, Bashir; Nieto, Juan J.; Alsaedi, Ahmed; Mohamad, Nadia

On a new class of antiperiodic fractional boundary value problems. (English) Zbl 1277.34005

Abstr. Appl. Anal. 2013, Article ID 606454, 7 p. (2013).
Summary: This paper investigates a new class of antiperiodic boundary value problems of higher-order fractional differential equations. Some existence and uniqueness results are obtained by applying some standard fixed-point principles. Some examples are given to illustrate the results.

Cited in 4 Documents

MSC:

34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations

Keywords:

higher-order fractional differential equations; fixed-point principles; antiperiodic boundary value problems
Cite Review PDF
Full Text: DOI
Creative Commons CC license icon Creative Commons BY license icon

References:

[1] Samko, S. G.; Kilbas, A. A.; Marichev, O. I., Fractional Integrals and Derivatives, Theory and Applications (1993), Yverdon, Switzerland: Gordon and Breach, Yverdon, Switzerland · Zbl 0818.26003
[2] Podlubny, I., Fractional Differential Equations, 198 (1999), San Diego, Calif, USA: Academic Press, San Diego, Calif, USA · Zbl 0918.34010
[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 (2006), Amsterdam, The Netherlands: Elsevier Science, Amsterdam, The Netherlands · Zbl 1092.45003 · doi:10.1016/S0304-0208(06)80001-0
[4] Sabatier, J.; Agrawal, O. P.; Machado, J. A. T., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, (2007), Dordrecht, The Netherlands: Springer, Dordrecht, The Netherlands · Zbl 1116.00014
[5] Baleanu, D.; Diethelm, K.; Scalas, E.; Trujillo, J. J., Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, 3 (2012), Boston, Mass, USA: World Scientific, Boston, Mass, USA · Zbl 1248.26011 · doi:10.1142/9789814355216
[6] Bai, Z., On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Analysis: Theory, Methods and Applications A, 72, 2, 916-924 (2010) · Zbl 1187.34026 · doi:10.1016/j.na.2009.07.033
[7] Gafiychuk, V.; Datsko, B., Mathematical modeling of different types of instabilities in time fractional reaction-diffusion systems, Computers and Mathematics with Applications, 59, 3, 1101-1107 (2010) · Zbl 1189.35151 · doi:10.1016/j.camwa.2009.05.013
[8] Băleanu, D.; Mustafa, O. G., On the global existence of solutions to a class of fractional differential equations, Computers and Mathematics with Applications, 59, 5, 1835-1841 (2010) · Zbl 1189.34006 · doi:10.1016/j.camwa.2009.08.028
[9] Băleanu, D.; Mustafa, O. G.; O’Regan, D., A Nagumo-like uniqueness theorem for fractional differential equations, Journal of Physics A, 44, 39 (2011) · Zbl 1229.26013 · doi:10.1088/1751-8113/44/39/392003
[10] Ahmad, B.; Nieto, J. J., Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions, Boundary Value Problems, 2011, 36 (2011) · Zbl 1275.45004
[11] Ahmad, B.; Ntouyas, S. K., A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order, Electronic Journal of Qualitative Theory of Differential Equations, 2011, 22 (2011) · Zbl 1340.34063
[12] Ford, N. J.; Morgado, M. L., Fractional boundary value problems: analysis and numerical methods, Fractional Calculus and Applied Analysis, 14, 4, 554-567 (2011) · Zbl 1273.65098 · doi:10.2478/s13540-011-0034-4
[13] Aghajani, A.; Jalilian, Y.; Trujillo, J. J., On the existence of solutions of fractional integro-differential equations, Fractional Calculus and Applied Analysis, 15, 1, 44-69 (2012) · Zbl 1279.45008 · doi:10.2478/s13540-012-0005-4
[14] Ahmad, B.; Ntouyas, S. K., A note on fractional differential equations with fractional separated boundary conditions, Abstract and Applied Analysis, 2012 (2012) · Zbl 1244.34004 · doi:10.1155/2012/818703
[15] Datsko, B.; Gafiychuk, V., Complex nonlinear dynamics in subdiffusive activator-inhibitor systems, Communications in Nonlinear Science and Numerical Simulation, 17, 4, 1673-1680 (2012) · Zbl 1244.35158 · doi:10.1016/j.cnsns.2011.08.037
[16] Ahmad, B.; Nieto, J. J.; Alsaedi, A.; El-Shahed, M., A study of nonlinear Langevin equation involving two fractional orders in different intervals, Nonlinear Analysis: Real World Applications, 13, 2, 599-606 (2012) · Zbl 1238.34008 · doi:10.1016/j.nonrwa.2011.07.052
[17] Ahmad, B.; Nieto, J. J., Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory, Topological Methods in Nonlinear Analysis, 35, 2, 295-304 (2010) · Zbl 1245.34008
[18] Ahmad, B., Existence of solutions for fractional differential equations of order \(q∈\) (2,3] with anti-periodic boundary conditions, Journal of Applied Mathematics and Computing, 34, 1-2, 385-391 (2010) · Zbl 1216.34003 · doi:10.1007/s12190-009-0328-4
[19] Agarwal, R. P.; Ahmad, B., Existence of solutions for impulsive anti-periodic boundary value problems of fractional semilinear evolution equations, Dynamics of Continuous, Discrete and Impulsive Systems A, 18, 4, 457-470 (2011) · Zbl 1226.26005
[20] Ahmad, B., New results for boundary value problems of nonlinear fractional differential equations with non-separated boundary conditions, Acta Mathematica Vietnamica, 36, 3, 659-668 (2011) · Zbl 1247.34004
[21] Wang, G.; Ahmad, B.; Zhang, L., Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear Analysis: Theory, Methods and Applications A, 74, 3, 792-804 (2011) · Zbl 1214.34009 · doi:10.1016/j.na.2010.09.030
[22] Ahmad, B.; Nieto, J. J., Anti-periodic fractional boundary value problems, Computers and Mathematics with Applications, 62, 3, 1150-1156 (2011) · Zbl 1228.34010 · doi:10.1016/j.camwa.2011.02.034
[23] Chen, Y.; Nieto, J. J.; O’Regan, D., Anti-periodic solutions for evolution equations associated with maximal monotone mappings, Applied Mathematics Letters, 24, 3, 302-307 (2011) · Zbl 1215.34069 · doi:10.1016/j.aml.2010.10.010
[24] Ahmad, B.; Nieto, J. J., Anti-periodic fractional boundary value problems with nonlinear term depending on lower order derivative, Fractional Calculus and Applied Analysis, 15, 3, 451-462 (2012) · Zbl 1281.34005 · doi:10.2478/s13540-012-0032-1
[25] Smart, D. R., Fixed Point Theorems (1974), Cambridge, UK: Cambridge University Press, Cambridge, UK · Zbl 0297.47042
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.