An application of fixed point theory in existence of solutions for fractional differential equations

An application of fixed point theory in existence of solutions for fractional differential equations

Abstract. In this paper, some new existense and uniqueness results for fractional differential equation are obtained by using fixed point theorems. We study the ex­istence of solution for the nonlinear fractional differential equation boundary value problem.

___

  • B. Samet, C. Vetro, P. Vetro, Fixed point theorems for a - ψ- contractive type mappings, J. Nonlinear Analysis: Theory, Methods &Applications, Vol. 75, (2012) 2154-2165.
  • KS. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation, New York: John Wiley; 1993.
  • KB. Oldham, J. Spainer, The Fractional Calculus, New York: Academic Press; 1974.
  • I. Podlubny, Fractional Differential Equations, New York/Lindon/Toronto: Academic Press; 1999.
  • SG. Samko, AA. Kilbas, OI. Marichev, Fractional Integral and Derivative, Theory and Applications. Switzerland: Gordon and Breach; 1993.
  • RP. Agarwal, Formulation of Euler-Lagrange equations for fractional variational problems, J. Math Anal Appl (2002); 272: 368-379.
  • H. Weitzner, GM. Zaslavsky, Some applications of fractional equations, Commun Nonlinear SciNumerSimul (2010); 15(4):939-45.
  • D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation,J. Math Anal Appl 204 (1996) 609-25.
  • S. Zhang, The existense of a positive solution for nonlinear fractional differential equation, J. Math. Analysis Appl. 252 (2000) 804-12.
  • S. Zhang, Existence of positive solutions for some class of nonlinear fractional equation, J. Math Anal Appl 278 (2003) 136-48.
  • I. Hashim, 0. Abdulaziz, S. Momani, Homotopy analysis method for fractional IVPs, Commun Nonlinear SciNumerSimul (2009): 14(3) : 674-84.
  • M. Al-Mdallal, MI. Syam, MN. Anwar, A collocation-shooting method for solving fractional boundary value problems, Commun Nonlinear SciNumerSimul (2010) ;15(12): 3814-22.
  • H. Jafari, V. Daftardar-Gejji, Positive solution of nonlinear fractional boundary value problems using Adomin decomposition method, J. Appl Math Comput (2006); 180: 700- 6.