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EXISTENCE OF POSITIVE SOLUTIONS FOR A COUPLED SYSTEM OF HIGHER ORDER FRACTIONAL BOUNDARY VALUE PROBLEMS

Yıl 2016, Cilt: 6 Sayı: 2, 278 - 288, 01.12.2016

Öz

The aim of this paper is to establish the existence of at least one positive solution for a coupled system of higher order two-point fractional order boundary value problems under suitable conditions. The approach is based on the Guo-Krasnosel'skii fixed point theorem.

Kaynakça

  • Agarwal,R.P., O’Regan,D. and Wong,P.J.Y., (1999), Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands.
  • Ahmed,B. and Nieto,J.J., (2009), Existence results for a coupled system of nonlinear fractional differ- ential equations with three-point boundary conditions, Comput. Math. Appl., 58, pp. 1838-1843.
  • Bai,Z. and L¨u,H., (2005), Positive solutions for boundary value problems of nonlinear fractional dif- ferential equations, J. Math. Anal. Appl., 311, pp. 495-505.
  • Benchohra,M., Henderson,J., Ntoyuas,S.K. and Ouahab,A., (2008), Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338, pp. 1340-1350.
  • Davis,J.M., Henderson,J., Prasad,K.R. and Yin,W., (2000), Eigenvalue intervals for non-linear right focal problems, Appl. Anal., 74, pp. 215-231.
  • Erbe,L.H. and Wang,H., (1994), On the existence of positive solutions of ordinary differential equa- tions, Proc. Amer. Math. Soc., 120, pp. 743-748.
  • Guo,D. and Lakshmikantham,V., (1988), Nonlinear Problems in Abstract Cones, Acadamic Press, San Diego.
  • Henderson,J. and Ntouyas,S.K., (2007), Positive solutions for systems of nthorder three-point nonlocal boundary value problems, Elec. J. Qual. Theory Diff. Equ., 18, pp. 1-12.
  • Henderson,J. and Ntouyas,S.K., (2008), Positive solutions for systems of nonlinear boundary value problems, Nonlinear Stud., 15, pp. 51-60.
  • Henderson,J., Ntouyas,S.K. and Purnaras,I.K., (2008), Positive solutions for systems of generalized three-point nonlinear boundary value problems, Comment. Math. Univ. Carolin., 49, pp. 79-91.
  • Kauffman,E.R. and Mboumi,E., (2008), Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Elec. J. Qual. Theory Diff. Equ., 2008, pp. 1-11.
  • Khan,R.A., Rehman,M. and Henderson,J., (2011), Existence and uniqueness of solutions for nonlinear fractional differential equations with integral boundary conditions, Fract. Differ. Calc., 1, pp. 29-43.
  • Kilbas,A.A., Srivasthava,H.M. and Trujillo,J.J., (2006), Theory and Applications of Fractional Differ- ential Equations, North-Holland Mathematics Studies, 204, Elsevier Science, Amserdam.
  • Krasnosel’skii,M.A., (1964), Positive Solutions of Operator Equations, Noordhoff, Groningen.
  • Podulbny,I., (1999), Fractional Diffrential Equations, Academic Press, San Diego.
  • Prasad,K.R. and Krushna,B.M.B., (2013), Multiple positive solutions for a coupled system of Riemann
  • Liouville fractional order two-point boundary value problems, Nonlinear Stud., 20, pp. 501-511. Prasad,K.R. and Krushna,B.M.B., (2014), Eigenvalues for iterative systems of Sturm–Liouville frac- tional order two-point boundary value problems, Fract. Calc. Appl. Anal., 17, DOI: 10.2478/s13540- 0190-4, pp. 638-653.
  • Prasad,K.R. and Krushna,B.M.B., (2015), Lower and upper solutions for general two-point fractional order boundary value problems, TWMS J. App. Eng. Math., 5, pp. 80-87.
  • Kapula Rajendra Prasad, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.3, No.2, 2013.
  • Boddu Muralee Bala Krushna, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.5, No.1, 2015.
Yıl 2016, Cilt: 6 Sayı: 2, 278 - 288, 01.12.2016

Öz

Kaynakça

  • Agarwal,R.P., O’Regan,D. and Wong,P.J.Y., (1999), Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands.
  • Ahmed,B. and Nieto,J.J., (2009), Existence results for a coupled system of nonlinear fractional differ- ential equations with three-point boundary conditions, Comput. Math. Appl., 58, pp. 1838-1843.
  • Bai,Z. and L¨u,H., (2005), Positive solutions for boundary value problems of nonlinear fractional dif- ferential equations, J. Math. Anal. Appl., 311, pp. 495-505.
  • Benchohra,M., Henderson,J., Ntoyuas,S.K. and Ouahab,A., (2008), Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338, pp. 1340-1350.
  • Davis,J.M., Henderson,J., Prasad,K.R. and Yin,W., (2000), Eigenvalue intervals for non-linear right focal problems, Appl. Anal., 74, pp. 215-231.
  • Erbe,L.H. and Wang,H., (1994), On the existence of positive solutions of ordinary differential equa- tions, Proc. Amer. Math. Soc., 120, pp. 743-748.
  • Guo,D. and Lakshmikantham,V., (1988), Nonlinear Problems in Abstract Cones, Acadamic Press, San Diego.
  • Henderson,J. and Ntouyas,S.K., (2007), Positive solutions for systems of nthorder three-point nonlocal boundary value problems, Elec. J. Qual. Theory Diff. Equ., 18, pp. 1-12.
  • Henderson,J. and Ntouyas,S.K., (2008), Positive solutions for systems of nonlinear boundary value problems, Nonlinear Stud., 15, pp. 51-60.
  • Henderson,J., Ntouyas,S.K. and Purnaras,I.K., (2008), Positive solutions for systems of generalized three-point nonlinear boundary value problems, Comment. Math. Univ. Carolin., 49, pp. 79-91.
  • Kauffman,E.R. and Mboumi,E., (2008), Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Elec. J. Qual. Theory Diff. Equ., 2008, pp. 1-11.
  • Khan,R.A., Rehman,M. and Henderson,J., (2011), Existence and uniqueness of solutions for nonlinear fractional differential equations with integral boundary conditions, Fract. Differ. Calc., 1, pp. 29-43.
  • Kilbas,A.A., Srivasthava,H.M. and Trujillo,J.J., (2006), Theory and Applications of Fractional Differ- ential Equations, North-Holland Mathematics Studies, 204, Elsevier Science, Amserdam.
  • Krasnosel’skii,M.A., (1964), Positive Solutions of Operator Equations, Noordhoff, Groningen.
  • Podulbny,I., (1999), Fractional Diffrential Equations, Academic Press, San Diego.
  • Prasad,K.R. and Krushna,B.M.B., (2013), Multiple positive solutions for a coupled system of Riemann
  • Liouville fractional order two-point boundary value problems, Nonlinear Stud., 20, pp. 501-511. Prasad,K.R. and Krushna,B.M.B., (2014), Eigenvalues for iterative systems of Sturm–Liouville frac- tional order two-point boundary value problems, Fract. Calc. Appl. Anal., 17, DOI: 10.2478/s13540- 0190-4, pp. 638-653.
  • Prasad,K.R. and Krushna,B.M.B., (2015), Lower and upper solutions for general two-point fractional order boundary value problems, TWMS J. App. Eng. Math., 5, pp. 80-87.
  • Kapula Rajendra Prasad, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.3, No.2, 2013.
  • Boddu Muralee Bala Krushna, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.5, No.1, 2015.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

K. R. Prasad Bu kişi benim

B. M. B. Krushna Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 2

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