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

Year 2015, Volume: 36 Issue: 3, 2572 - 2577, 13.05.2015

Akbar Azamı , Hakimeh Mohammadı

Abstract

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.

 

With Caputo fractional derivative and Riemann-Liouville fractional derivative and different boundary value

 

and

x(O) = 0, x(l) = x(s) ds, 0 <<1.

Keywords

Boundary value problem fixed point Fractional differential inclusion

References

  • 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.

Year 2015, Volume: 36 Issue: 3, 2572 - 2577, 13.05.2015

Akbar Azamı , Hakimeh Mohammadı

Abstract

References

  • 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.
There are 13 citations in total.

Details

Journal Section Special
Authors

Akbar Azamı

Hakimeh Mohammadı This is me

Publication Date May 13, 2015
Published in Issue Year 2015 Volume: 36 Issue: 3

Cite

APA Azamı, A., & Mohammadı, H. (2015). An application of fixed point theory in existence of solutions for fractional differential equations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 36(3), 2572-2577.
AMA Azamı A, Mohammadı H. An application of fixed point theory in existence of solutions for fractional differential equations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. May 2015;36(3):2572-2577.
Chicago Azamı, Akbar, and Hakimeh Mohammadı. “An Application of Fixed Point Theory in Existence of Solutions for Fractional Differential Equations”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36, no. 3 (May 2015): 2572-77.
EndNote Azamı A, Mohammadı H (May 1, 2015) An application of fixed point theory in existence of solutions for fractional differential equations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36 3 2572–2577.
IEEE A. Azamı and H. Mohammadı, “An application of fixed point theory in existence of solutions for fractional differential equations”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, pp. 2572–2577, 2015.
ISNAD Azamı, Akbar - Mohammadı, Hakimeh. “An Application of Fixed Point Theory in Existence of Solutions for Fractional Differential Equations”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36/3 (May 2015), 2572-2577.
JAMA Azamı A, Mohammadı H. An application of fixed point theory in existence of solutions for fractional differential equations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36:2572–2577.
MLA Azamı, Akbar and Hakimeh Mohammadı. “An Application of Fixed Point Theory in Existence of Solutions for Fractional Differential Equations”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, 2015, pp. 2572-7.
Vancouver Azamı A, Mohammadı H. An application of fixed point theory in existence of solutions for fractional differential equations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36(3):2572-7.