Existence of positive solutions for N-term non-autonomous fractional differential equations

Positivity

Volumn 9, Issue 2, 2005, Pages 193-206

  Babakhani, A ^a   Daftardar Gejji, Varsha ^a  

^a UNIVERSITY OF PUNE   (India)

Author keywords

Completely continuous operator; Equicontinuous set; Normal cone; Riemann Liouville fractional derivatives and integrals; Semi ordered Banach space

Indexed keywords

EID: 27244434446     PISSN: 13851292     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11117-005-2715-x     Document Type: Article

References (13)

1. Samko, S., Kilbas, A. and Marichev, O.: Fractional Integrals and Derivatives. Gordon and Breach Science Publishers, Singapore, 1993.
2. Podlubny, I.: Fractional Differential Equations. Academic Press, London, 1999.
3. Miller, K. V, and Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley-Interscience, New York, 1993.
4. Mainardi, F.: Fractional Calculus: Some basic problems in continuum and statistical mechanics, in Fractals and Fractional Calculus in Continuum Mechanics, Carpinteri, A. and Mainardi, F. (eds), Springer, New York, 1997.
5. Delbosco, D. and Rodino, L.: Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl. 204 (1996), 609-625.
6. Diethelm, K. and Ford, N. J: Analysis of Fractional Differential Equations, J. Math. Anal. Appl. 265 (2002), 229-248.
7. Agarwal, R. P. and O'Regan, D.: Positive solutions for (p, n-p) conjugate boundary value problems, J. Diff. Equations 150 (1998) 462-473.
8. Erbe, L. H. and Wang, H.: On the existence of positive solutions of ordinary differential equations, Proc. Am. Math. Soc. 120 (1994) 743-748.
9. Chyan, C. J. and Henderson, J.: Positive solutions of 2m-th order boundary value problems, Applied Mathematics Letters 15 (2002) 767-774.
10. Zhang, S.: The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl. 252 (2000), 804-812.
11. Joshi, M. C. and Bose, R. K.: Some Topics in Nonlinear Functional Analysis. Wiley Eastern Limited, New Delhi, 1985.
12. Goldberg, R. R.: Methods of Real Analysis. Oxford and IBH Publishing Company, New Delhi, 1970.
13. Aliprantis, C. D. and Burkinshaw, O.: Principles of Real Analysis, Second Edition, Academic Press, New York, 1990.