SOLUTIONS FOR A FRACTIONAL-ORDER DIFFERENTIAL
EQUATION WITH BOUNDARY CONDITIONS OF THIRD ORDER

Abstract

This paper is concerned with a fractional-order boundary value problem involving the Riemann-Liouville fractional derivative of order $\alpha \in (3,4]$. Existence and uniqueness results of solutions are established by the Banach fixed point theorem.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 3
Year: 2020

DOI: 10.12732/ijam.v33i3.4

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References

  1. [1] Z. Bai and H. L¨u, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311, No 2 (2005), 495-505.
  2. [2] M. Benchohra, N. Hamidi and J. Henderson, Fractional differential equations with anti-periodic boundary condition, Numer. Funct. Anal. Optim. 34, No 4 (2013), 404-414.
  3. [3] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Ser. North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
  4. [4] T. F. Ma and J. da Silva, Iterative solutions for a beam equation with nonlinear boundary conditions of third order, Appl. Math. Comput. 159, No 1 (2004), 11-18.
  5. [5] M. Toyoda and T. Watanabe, Note on solutions of boundary value problems involving a fractional differential equation, Linear Nonlinear Anal. 3, No 3 (2017), 449-455.