Positive solutions for a system of fractional boundary value problems
Henderson, Johnny; Luca, Rodica
- Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 1-10
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topHenderson, Johnny, and Luca, Rodica. "Positive solutions for a system of fractional boundary value problems." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 1-10. <http://eudml.org/doc/294943>.
@inProceedings{Henderson2017,
abstract = {We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with nonnegative nonlinearities which can be nonsingular or singular functions, subject to multi-point boundary conditions that contain fractional derivatives.},
author = {Henderson, Johnny, Luca, Rodica},
booktitle = {Proceedings of Equadiff 14},
keywords = {Riemann-Liouville fractional differential equations, multi-point boundary conditions, positive solutions, existence},
location = {Bratislava},
pages = {1-10},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Positive solutions for a system of fractional boundary value problems},
url = {http://eudml.org/doc/294943},
year = {2017},
}
TY - CLSWK
AU - Henderson, Johnny
AU - Luca, Rodica
TI - Positive solutions for a system of fractional boundary value problems
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 1
EP - 10
AB - We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with nonnegative nonlinearities which can be nonsingular or singular functions, subject to multi-point boundary conditions that contain fractional derivatives.
KW - Riemann-Liouville fractional differential equations, multi-point boundary conditions, positive solutions, existence
UR - http://eudml.org/doc/294943
ER -
References
top- Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, , SIAM Review, 18 (1976), pp. 620–709. MR0415432
- Arafa, A. A. M., Rida, S. Z., Khalil, M., Fractional modeling dynamics of HIV and CD4 T-cells during primary infection, , Nonlinear Biomed. Phys., 6 (1) (2012), pp. 1–7. MR3225564
- Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J. J., Fractional Calculus Models and Numerical Methods, , Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston,2012. MR2894576
- Cole, K., Electric conductance of biological systems, , in: Proc. Cold Spring Harbor Symp. Quant. Biol., Col Springer Harbor Laboratory Press, New York, 1993, pp. 107–116.
- Das, S., Functional Fractional Calculus for System Identification and Controls, , Springer, New York, 2008. MR2414740
- Ding, Y., Ye, H., A fractional-order differential equation model of HIV infection of CD4 T-cells, , Math. Comp. Model., 50 (2009), pp. 386–392. MR2542785
- Djordjevic, V., Jaric, J., Fabry, B., Fredberg, J., Stamenovic, D., Fractional derivatives embody essential features of cell rheological behavior, , Ann. Biomed. Eng., 31 (2003), pp. 692–699.
- Ge, Z. M., Ou, C. Y., Chaos synchronization of fractional order modified Duffing systems with parameters excited by a chaotic signal, , Chaos Solitons Fractals, 35 (2008), pp. 705–717.
- Guo, D., Lakshmikantham, V., Nonlinear Problems in Abstract Cones, , Academic Press, New York, 1988. MR0959889
- Henderson, J., Luca, R., Existence and multiplicity of positive solutions for a system of fractional boundary value problems, , Bound. Value Probl., 2014:60 (2014), pp. 1–17. MR3352633
- Henderson, J., Luca, R., Positive solutions for a system of fractional differential equations with coupled integral boundary conditions, , Appl. Math. Comput., 249 (2014), pp. 182–197. MR3279412
- Henderson, J., Luca, R., Nonexistence of positive solutions for a system of coupled fractional boundary value problems, , Bound. Value Probl., 2015:138 (2015), pp. 1–12. MR3382857
- Henderson, J., Luca, R., Positive solutions for a system of semipositone coupled fractional boundary value problems, , Bound. Value Probl., 2016(61) (2016), pp. 1–23. MR3471318
- Henderson, J., Luca, R., Boundary Value Problems for Systems of Differential, Difference and Fractional Equations, , Positive Solutions, Elsevier, Amsterdam, 2016. MR3430818
- Henderson, J., Luca, R., Existence of positive solutions for a singular fractional boundary value problem, , Nonlinear Anal. Model. Control, 22(1) (2017), pp. 99–114. MR3594626
- Henderson, J., Luca, R., Tudorache, A., On a system of fractional differential equations with coupled integral boundary conditions, , Fract. Calc. Appl. Anal., 18(2) (2015), pp. 361–386. MR3323907
- Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and Applications of Fractional Differential Equations, , North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006. MR2218073
- Klafter, J., Lim, S. C., (Eds.), R. Metzler, Fractional Dynamics in Physics, Singapore, , World Scientific, 2011. MR2920446
- Luca, R., Tudorache, A., Positive solutions to a system of semipositone fractional boundary value problems, , Adv. Difference Equ., 2014(179) (2014), pp. 1–11. MR3357337
- Metzler, R., Klafter, J., The random walks guide to anomalous diffusion: a fractional dynamics approach, , Phys. Rep., 339 (2000), pp. 1–77. MR1809268
- Ostoja-Starzewski, M., Towards thermoelasticity of fractal media, , J. Therm. Stress., 30 (2007), pp. 889–896.
- Podlubny, I., Fractional Differential Equations, , Academic Press, San Diego, 1999. MR1658022
- Povstenko, Y.Z., Fractional Thermoelasticity, , New York, Springer, 2015. MR3287225
- Sabatier, J., Agrawal, O. P., (Eds.), J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, , Springer, Dordrecht, 2007. MR2432163
- Samko, S. G., Kilbas, A. A., Marichev, O. I., Fractional Integrals and Derivatives, , Theory and Applications, Gordon and Breach, Yverdon, 1993. MR1347689
- Sokolov, I. M., Klafter, J., Blumen, A., A fractional kinetics, , Phys. Today, 55 (2002), pp. 48–54.
- Zhou, Y., Xu, Y., Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations, , J. Math. Anal. Appl., 320 (2006), pp. 578–590. MR2225977
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