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UPPER AND LOWER SOLUTION METHOD FOR FRACTIONAL EVOLUTION EQUATIONS WITH ORDER 1 < α < 2

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In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with or- der 1 < α < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

Abstract

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with or- der 1 < α < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

참고문헌 (34)

  1. S. Abbas, "Upper and lower solutions method for darboux problem for fractional order implicit impulsive partial hyperbolic differential equations", Acta Univ. Palacki. Olomuc. Fac. Rer. Nat. Mathematica, 51(2), pp.5~18 (2012)
  2. R. P. Agarwal, "Existence results for differential equations with fractional order and impulses", Mem. Differential Equations Math. Phys, 44, pp.1~21 (2008)
  3. B. Ahmad, "Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations", Nonlinear Anal. Hybrid Syst, 3(3), pp.251~258 (2009)
  4. B. Ahmad, "Existence of solutions for impulsive integral boundary value problems of fractional order", Nonlinear Anal. Hybrid Syst, 4(1), pp.134~141 (2010)
  5. K. Balachandran, "Existence of solutions of abstract fractional impulsive semilinear evolution equations", Electron. J. Qual. Theory Differ. Equ, 4(4), pp.12~ (2010)
  6. J. Bana's, "Measure of Noncompactness in Banach Spaces" (1980), Marcel Dekker Inc.
  7. E. Bazhlekova, "Fractional evolution equations in Banach spaces", Ph.D., pp.2001
  8. R. Bellman, "The stability of solutions of linear differential equations", Duke Math. J, 10(4), pp.643~647 (1943)
  9. M. Belmekki, "Existence result for fractional order semilinear functional differential equations with nondense domain", Nonlinear Anal, 72(2), pp.925~932 (2010)
  10. M. Benchohra, "Existence results for fractional functional differential inclusions with infinite delay and application to control theory", Fract. Calc. Appl. Anal, 11(1), pp.35~56 (2008)
  11. M. Benchohra, "Existence and uniqueness of solutions to impulsive fractional differential equations", Electron. J. Differential Equations, 2009(10), pp.11~ (2009)
  12. P. Benilan, "Equations d'evolution dans un espace de Banach quelconque et applications", doctor, pp.1972
  13. D. Bothe, "Multivalued perturbation of m-accretive differential inclusions", lsrael. J. Math, 108, pp.109~138 (1998)
  14. K. Deimling, "Nonlinear Functional Analysis" (1985), Springer-Verlag
  15. Z. Denton, "Quasilinearization method via lower and upper solutions for Riemann-Liouville fractional differential equations", Nonlinear Dyn. Syst. Theory, 11(3), pp.239~251 (2011)
  16. H. Fan, "Initial value problem for fractional evolution equations", Adv. Difference Equ, 2012(49), pp.10~ (2012)[DOI]
  17. D. J. Guo, "Nonlinear Integral Equations in Abstract Spaces" (1996), Kluwer Academic
  18. H.-P. Heinz, "On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions", Nonlinear Anal, 7(12), pp.1351~1371 (1983)
  19. L. Hu, "Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays", Semigroup Forum, 79(3), pp.507~514 (2009)
  20. R. W. Ibrahim, "Upper and lower bounds of solutions for fractional integral equations", Surv. Math. Appl, 2, pp.145~156 (2007)
  21. O. K. Jaradat, "Existence of the mild solution for fractional semilinear initial value problems", Nonlinear Anal, 69(9), pp.3153~3159 (2008)
  22. V. Lakshmikantham, "Nonlinear Differential Equations in Abstract Spaces" (1969), Pergamon Press
  23. L. Lin, "Method of upper and lower solutions for fractional differential equations", Electron. J. Differential Equations, 2012(100), pp.13~ (2012)
  24. F. Mainardi, "Probability distributions generated by fractional diffusion equations" (2000), Kluwer
  25. H. Monch, "Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces", Nonlinear Anal, 4(5), pp.985~999 (1980)
  26. G. M. Mophou, "Existence and uniqueness of mild solutions to impulsive fractional differential equations", Nonlinear Anal, 72(304), pp.1604~1615 (2010)
  27. J. Mu, "Monotone iterative technique for fractional evolution equations in Banach spaces", J. Appl. Math, 2011, pp.13~ (2011)
  28. I. Podlubny, "Fractional Differential Equations" (1999), Academic Press
  29. X. Shu, "The existence of mild solutions for impulsive fractional partial differential equations", Nonlinear Anal, 74(5), pp.2003~2011 (2011)
  30. X. Shu, "The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1 < α < 2", Comput. Math. Appl, 64(6), pp.2100~2110 (2012)
  31. Z. Tai, "Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces", Appl. Math. Lett, 22(11), pp.1760~1765 (2009)
  32. C. Wang, "On positive solution of nonlinear fractional differential equation", World Appl. Sci. J, 18(11) (2012)
  33. A. Yakar, "Initial time difference quasilinearization for Caputo fractional differential equations", Adv. Difference Equ, 2012(92), pp.9~ (2012)
  34. S. Zhang, "Existence of extreme solutions for fractional order boundary value problem using upper and lower solutions method in reverst order", J. Fract. Calc. Appl, 2(6), pp.1~14 (2012)

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