PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Existence of three solutions for impulsive nonlinear fractional boundary value problems

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.
Rocznik
Strony
281--301
Opis fizyczny
Bibliogr. 53 poz.
Twórcy
  • Razi University Faculty of Sciences Department of Mathematics 67149 Kermanshah, Iran
autor
  • University Mediterranea of Reggio Calabria Department of Law and Economics Via dei Bianchi, 2 - 89131 Reggio Calabria, Italy
autor
  • University of Messina Department of Economics Via dei Verdi, 75, Messina, Italy
autor
  • Razi University Faculty of Sciences Department of Mathematics 67149 Kermanshah, Iran
Bibliografia
  • [1] C. Bai, Existence of solutions for a nonlinear fractional boundary value problem via a local minimum theorem, Electron. J. Differ. Equ. 2012 (2012) 176, 1-9.
  • [2] C. Bai, Infinitely many solutions for a perturbed nonlinear fractional boundary value-problem, Electron. J. Differ. Equ. 2013 (2013) 136, 1-12.
  • [3] C. Bai, Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Eqs. 2011 (2011) 89, 1-19.
  • [4] D. Bainov, P. Simeonov, Systems with Impulse Effect, Ellis Horwood Series: Mathematics and Its Applications, Ellis Horwood, Chichester, 1989.
  • [5] M. Belmekki, J.J. Nieto, R. Rodriguez-López, Existence of periodic solution for a nonlinear fractional differential equation, Bound. Value Probl. 2009 (2009), Art. ID 324561,18 pp.
  • [6] M. Benchohra, A. Cabada, D. Seba, An existence result for nonlinear fractional differential equations on Banach spaces, Bound. Value Probl. 2009 (2009), Art. ID 628916, pp.
  • [7] M. Benchohra, J. Henderson, S.K. Ntouyas, Theory of Impulsive Differential Equations, Contemporary Mathematics and Its Applications, vol. 2, Hindawi Publishing Corporation, New York, 2006.
  • [8] G. Bonanno, R. Rodriguez-López, S. Tersian, Existence of solutions to boundary-value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal. 3 (2014), 717-744.
  • [9] H. Chen, Z. He, New results for perturbed Hamiltonian systems with impulses, Appl. Math. Comput. 1218 (2012), 9489-9497.
  • [10] J. Chen, X.H. Tang, Existence and multiplicity of solutions for some fractional boundary value problem via critical point theory, Abstr. Appl. Anal. 2012 (2012), 1-21.
  • [11] J.-N. Corvellec, V.V. Motreanu, C. Saccon, Doubly resonant semilinear elliptic problems via nonsmooth critical point theory, J. Differ. Equ. 248 (2010), 2064-2091.
  • [12] M. De la Sen, On Riemann-Liouville and Caputo impulsive fractional calculus, [in:] Proc. of the World Congress on Engineering 2011, vol. 1, London, UK, 2011.
  • [13] K. Diethelm, A.D. Freed, On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, [in:] F. Keil, W. Mackens, H. Voss, J. Werther (eds), Computing in Chemical Engineering, II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, Springer-Verlag, Heidelberg, 1999, 217-224.
  • [14] M. Ferrara, S. Heidarkhani, Multiple solutions for perturbed p-Laplacian boundary value problem with impulsive effects, Electron. J. Differ. Equ. 2014 (2014) 106, 1-14.
  • [15] M. Ferrara, G. Molica Bisci, Remarks for one-dimensional fractional equations, Opuscula Math. 34 (2014) 4, 691-698.
  • [16] M. Galewski, G. MolicaBisci, Existence results for one-dimensional fractional equations, Math. Meth. Appl. Sci. 39 (2016), 1480-1492.
  • [17] L. Gaul, P. Klien, S. Kempfle, Damping description involving fractional operators, Mech. Syst. Signal Pr. 5 (1991), 81-88.
  • [18] W.G. Glockle, T.F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophysical J. 68 (1995), 46-53.
  • [19] J.R. Graef, L. Kong, Q. Kong, Multiple solutions of systems of fractional boundary value problems, Appl. Anal. 94 (2015), 1288-1304.
  • [20] J.R. Graef, L. Kong, Q. Kong, M. Wang, Fractional boundary value problems with integral boundary conditions, Appl. Anal. 92 (2013), 2008-2020.
  • [21] S. Heidarkhani, Multiple solutions for a nonlinear perturbed fractional boundary value problem, Dynam. Sys. Appl. 23 (2014), 317-332.
  • [22] S. Heidarkhani, Infinitely many solutions for nonlinear perturbed fractional boundary value problems, Annals of the University of Craiova, Math. Comput. Sci. Ser. 41 (2014) 1, 88-103
  • [23] S. Heidarkhani, M. Ferrara, A. Salari, Infinitely many periodic solutions for a class of perturbed second-order differential equations with impulses, Acta. Appl. Math. 139 (2015), 81-94.
  • [24] S. Heidarkhani, A. Salari, Existence of three solutions for impulsive perturbed elastic beam fourth-order equations of Kirchhoff-type, Stud. Sci. Math. Hungarica, to appear.
  • [25] S. Heidarkhani, A. Salari, Nontrivial Solutions for impulsive fractional differential systems through variational methods, Comput. Math. Appl. (2016), http://dx.doi.Org/10.1016/j.camwa.2016.04.016.
  • [26] S. Heidarkhani, Y. Zhao, G. Caristi, G.A. Afrouzi, S. Moradi, Infinitely many solutions for perturbed impulsive fractional differential systems, Appl. Anal. (2016), http://dx.doi.org/10.1080/00036811.2016.1192147.
  • [27] S. Heidarkhani, Y. Zhou, G. Caristi, G.A. Afrouzi, S. Moradi, Existence results for fractional differential systems through a local minimization principle, Comput. Math. Appl. (2016), http://dx.doi.Org/10.1016/j.camwa.2016.04.012.
  • [28] R. Hilferm, Applications of Fractional Calculus in Physics, World Scientific, Singapore,
  • 2000.
  • [29] F. Jiao, Y. Zhou, Existence of solutions for a class of fractional boundary value problems via critical point theory, Comput. Math. Appl. 62 (2011), 1181-1199.
  • [30] T.D. Ke, D. Lan, Decay integral solutions for a class of impulsive fractional differential equations in Banach spaces, Fract. Calc. Appl. Anal. 17 (2014) 1, 96-121.
  • [31] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  • [32] L. Kong, Existence of solutions to boundary value problems arising from the fractional advection dispersion equation, Electron. J. Diff. Equ. 2013 (2013) 106, 1-15.
  • [33] V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. TMA 69 (2008), 2677-2682.
  • [34] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of impulsive differential equations, Series in Modern Applied Mathematics, vol. 6, World Scientific, Teaneck, NJ, 1989.
  • [35] F. Li, Z. Liang, Q. Zhang, Existence of solutions to a class of nonlinear second order two-point boundary value problems, J. Math. Anal. Appl. 312 (2005), 357-373.
  • [36] X. Liu, A.R. Willms, Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft, Math. Probl. Eng. 2 (1996), 277-299.
  • [37] F. Mainardi, Fractional Calculus: some basic problems in continuum and statistical mechanics, [in:] A. Carpinteri, F. Maniardi (eds), Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, Wien, 1997, 291-348.
  • [38] J. Mawhin, M. Willem, Critical Point Theorey and Hamiltonian Systems, Springer, New York, 1989.
  • [39] F. Metzler, W. Schick, H.G. Kilan, T.F. Nonnenmacher, B,elaxation in filled polymers: A Fractional Calculus approach, J. Chemical Phys. 103 (1995), 7180-7186.
  • [40] G. Molica Bisci, Fractional equations with bounded primitive, Appl. Math. Lett. 27 (2014), 53-58.
  • [41] G. Molica Bisci, V. Radulescu, Ground state solutions of scalar field fractional Schrodinger equations, Calc. Var. Partial Differ. Equ. 54 (2015), 2985-3008.
  • [42] G. Molica Bisci, V. Radulescu, Multiplicity results for elliptic fractional equations with subcritical term, Nonlinear Differ. Equ. Appl. 22 (2015), 721-739.
  • [43] G. Molica Bisci, R. Servadei, A bifurcation result for non-local fractional equations, Anal. Appl. 13 (2015), 371-394.
  • [44] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [45] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, [in:] CBMS, vol. 65, American Mathematical Society, 1986.
  • [46] B. Ricceri, A further three critical points theorem, Nonlinear Anal. TMA 71 (2009), 4151-4157.
  • [47] R. Rodrfguez-López, S. Tersian, Multiple solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal. 17 (2014), 1016-1038.
  • [48] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integral and Derivatives: Theory and Applications, Gordon and Breach, Longhorne, PA, 1993.
  • [49] A.M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
  • [50] J. Sun, H. Chen, J.J. Nieto, M. Otero-Novoa, The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects, Nonlinear Anal. TMA 72 (2010), 4575-4586.
  • [51] Y. Tian, Z. Bai, Existence results for the three-point impulsive boundary value problem involving fractional differential equations, Comput. Math. Appl. 59 (2010), 2601-2609.
  • [52] J. Wang, M. Feckan, Y. Zhou, On the new concept of solutions and existence results for impulsive fractional evolution equations, Dynam. Part. Differ. Eqs. 58 (2011), 345-361.
  • [53] E. Zeidler, Nonlinear Functional Analysis and Its Applications, vol. II, Springer, Berlin-Heidelberg-New York, 1985.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-096f37cb-360a-4da2-a67d-f2ddaca3dd70
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.