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Existence of Positive Solutions for a Class of Conformable Fractional Differential Equations with Parameterized Integral Boundary Conditions

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In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green’s function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

Abstract

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green’s function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

참고문헌 (26)

  1. T. Abdeljawad, "On conformable fractional calculus", J. Comput. Appl. Math, 279, pp.57~66 (2015)
  2. M. Al Horani, "Total fractional differentials with applications to exact fractional differential equations", Int. J. Comput. Math, 95(6-7), pp.1444~1452 (2018)
  3. M. Al-Rifae, "Fundamental results of conformable Sturm-Liouville eigenvalue problems", Complexity, pp.7~ (2017)
  4. H. Amann, "Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces", SIAM. Rev, 18(4), pp.620~709 (1976)
  5. D. R. Anderson, "Fractional-order boundary value problem with SturmLiouville boundary conditions", Electron. J. Differential Equations, (29), pp.10~ (2015)
  6. D. R. Anderson, "Newly defined conformable derivatives", Adv. Dyn. Syst. Appl, 10, pp.109~137 (2015)
  7. D. R. Anderson, "Properties of the Katugampola fractional derivative with potential application in quantum mechanics", J. Math. Phys, 56(6), pp.18~ (2015)
  8. S. Asawasamrit, "Periodic boundary value problems for impulsive conformable fractional integro-differential equations", Bound. Value Probl, (122), pp.18~ (2016)
  9. A. Atangana, "Model of break-bone fever via beta-derivatives", BioMed Res. Int, pp.10~ (2014)
  10. H. Batarfi, "Three-point boundary value problems for conformable fractional differential equations", J. Funct. Spaces, pp.6~ (2015)
  11. B. Bayour, "Existence of solution to a local fractional nonlinear differential equation", J. Comput. Appl. Math, 312, pp.127~133 (2017)
  12. M. Caputo, "A new definition of fractional derivative without singular kernel", Progr. Fract. Differ. Appl, 2, pp.73~85 (2015)
  13. K. Deimling, "Nonlinear functional analysis" (1985), Springer
  14. X. Dong, "Positive solutions for nonlinear eigenvalue problems with conformable fractional differential derivatives", J. Shandong Univ. Sci. Tech. Nat. Sci, 35, pp.85~90 (2016)
  15. X. Dong, "Positive solutions to boundary value problems of pLaplacian with fractional derivative", Bound. Value Probl, (5), pp.15~ (2017)
  16. L. He, "Solvability of some two-point fractional boundary value problems under barrier strip conditions", J. Funct. Spaces, pp.6~ (2017)
  17. U. N. Katugampola, "A new fractional derivative with classical properties", arXiv:1410.6535, ~
  18. R. Khalil, "A new definition of fractional derivative", J. Comput. Appl. Math, 264, pp.65~70 (2014)
  19. K. Lan, "Positive solutions of semilinear differential equations with singularities", J. Differ. Equ, 148, pp.407~421 (1998)
  20. J. Losada, "Properties of a new fractional derivative without singular kernel", Progr. Fract. Differ. Appl, 1(2), pp.87~92 (2015)
  21. Q. Song, "Existence for fractional Dirichlet boundary value problem under barrier strip conditions", J. Nonlinear Sci. Appl, 10, pp.3592~3598 (2017)
  22. J. Weberszpil, "Variational approach and deformed derivatives", Phys. A, 450, pp.217~227 (2016)
  23. S. Yang, "Conformable derivative : Application to non-Darcian flow in low-permeability porous media", Appl. Math. Lett, 79, pp.105~110 (2018)
  24. D. Zhao, "General conformable fractional derivative and its physical interpretation", Calcolo, 54, pp.903~917 (2017)
  25. W. Zhong, "Positive solutions of conformable fractional differential equations with integral boundary conditions", Bound. Value Probl, (136), pp.12~ (2018)
  26. H. W. Zhou, "Conformable derivative approach to anomalous diffusion", Phys. A, 491, pp.1001~1013 (2018)

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