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
K. R. Prasad
B. M. B. Krushna
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
K. R. Prasad
B. M. B. Krushna
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.