NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SYSTEMS OF COUPLED FRACTIONAL BVPS WITH p-LAPLACIAN

Year 2019, Volume: 9 Issue: 3, 0 - 11, 01.09.2019

S. N. Rao M. Z. Meetei

Abstract

We investigate the nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional dierential equations with p-Laplacian two-point boundary value problem.

Keywords

Fractional order, Green's function, p-Laplacian, eigenvalue interval, nonexistence, cone.

References

• Agarwal, R. P. Zhou, Y. and He Y., (2010), Existence of fractional neutral functional differential equations, Comput. Math. Appl., 59, 1095-3554.
• Ahmad, B. Ntouyas, S. K., (2012), A note on fractional differential differential equations with frac- tional separated boundary conditions, Abstr. Appl. Anal., Article ID 818703, 1-11.
• Benchohra, M. Hamani, S. Henderson, J. Ntouyas, S. K. and Ouahab, A., (2007), Positive solutions for systems of nonlinear eigenvalue problems, Global. J. Math. Anal., 1, 19-28.
• Bai, Z., On positive solutions of a nonlocal fractional boundary value problem, (2010), Nonlinear Anal., 72, 916-924.
• Bai, Z. Lu, H., (2005), Positive solutions for boundary value problems of nonlinear fractional differ- ential equations, J. Math. Anal. Appl., 311, 495-505.
• Das, S., (2008), Functional Fractional Calculus for System Identification and Controls. Springer, New York.
• Henderson, J., Wang, H., (1997) Positive solutions for nonlinear eigenvalue problems, J. Math. Anal. Appl., 208, 252-259.
• Henderson, J. Luca, R., (2015) Nonexistence of positive solutions for a system of coupled fractional- boundary value problems, Bound. Value Probl., 138, doi: 10.1186/s13661-015-0403-8.
• Han, X. Gao, H., (2012) Existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations, Adv. Differ. Equ., 66.
• Kilbas, A. A. Srivastava, H. M. and Trujillo,J. J., (2016) Theory and Applications of Fractional Differential Equations., North-Holland Mathematics Studies, 204, Elsevier Science B. V., Amsterdam. [11] Luka, R. Deliu, C., (2013) Nonexistence of positive solutions for a system of higher-order multi-point boundary value problems, Romai J., 9, 69-77.
• Lu,H. Han, Z. and Sun,S., (2014) Multiplicity of positive solutions for Sturm-Liouville boundary value problems with p-Laplacian, Bound. Value Probl., 26, doi: 10.1186/1687-2770-2014-26.
• Liang, S. Zhang, J., (2009) Positive solutions for boundary value problems of nonlinear fractional differential equation, Nonlinear Anal., 71, 5545-5550.
• Rao,S. N. Prasad,K. R., (2015) Nonexistence of positive solutions for a system of nonlinear multi-point boundary value problems on time scales, Math. Commun., 20, 69-81.
• Rao,S. N., (2015) Existence and nonexistence of positive solutions for a system of even order dynamic equation on time scales, J. Appl. Math. and Informatics., 33, No. 5-6, 531-543.
• Nageswararao, S., (2015) Existence of positive solutions for RiemannLiouville fractional order three- point boundary value problem, Asian-Eur. J. Math., 8, No.4, doi: 10.1142/s 1793557115500576.
• Nageswararao, S., (2016) Existence and multiplicity for a system of fractional higher-order two-point boundary value problem, J. Appl. Math. Comput., 51, 93-107, doi: 10.1007/s 12190-015-0893-7.
• Rao,S. N., (2016) Multiplicity of Positive Solutions for Fractional Differential Equation with p- Laplacian Boundary Value Problems, Int. J. Differ. Equ., Article ID 6906049, 10 pages, DOI: 10.1155/2016/6906049.
• Nageswararao, S.,(2017) Solvability for a system of nonlinear fractional higher-order three-point boundary value problem. Fract. Differ. Calc., 7, No. 1, 151-167, doi:10.7153/fdc-07-04.
• Prasad, K. R, Rao,S. N, and Murali, P., (2009) Solvability of a nonlinear general third order two-point eigenvalue problem on time scales, Differ. Equ. Dyn. Syst., 17, No. 3, 269-282.
• Prasad, K. R, Rao, S. N. and Rao, A. K., (2010) Solvability for even-order three-point boundary value problems on time scales, Int. J. Appl. Math., 23, No. 1, 23-41.
• Podlubny, I., (1999) Fractional Differential Equations. Mathematics in Science and Engineering, Aca- demic Press, New York, 198.
• Sabatier, J. Agrawal, PO, and Machado, JAT., (2007) Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht.
• Shimoto, K.N., (1990) Fractional Calculus and its applications. Nihon University, koriyama.
• Tu, S. Nishimoto, K. and Jaw, S.,(1993) Applications of fractional calculus to ordinary and partial diffeential equations of second order, Hiroshima Math. J., 23, 63-67.