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Positive Solutions for Fractional Differential Equations with Multi-Point Boundary Value Problems

DOI: 10.4236/jamp.2014.25014, PP. 108-114

Keywords: Caputo Fractional Derivative, Fractional Integral, Boundary Value Problem, Fixed Point Index Theory

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Abstract:

In this paper, a fractional multi-point boundary value problem is considered. By using the fixed point index theory and Krein-Rutman theorem, some results on existence are obtained.

References

[1]  Kilbas, A.A., Srivastava Hari, M. and Trujillo Juan, J. (2006) Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studied, Vol. 204. Elsevier Science BV, Amsterdam.
[2]  Oldham, K.B. and Spanier, J. (1974) The Fractional Calculus. Academic Press, New York, London.
[3]  Ross, B. (1975) The Fractional Calculus and Its Applications. Lecture Notes in Mathematics, Vol. 475, Springer, Berlin.
[4]  Nonnenmacher, T.F. and Metzler, R. (1995) On the Riemann-Liouvile Fractional Calculus and Some Recent Applications. Fractals, 3, 557-566. http://dx.doi.org/10.1142/S0218348X95000497
[5]  Tatom, F.B. (1995) The Relationship between Fractional Calculus and Fractals. Fractals, 3, 217-229. http://dx.doi.org/10.1142/S0218348X95000175
[6]  Podlubny, I. (1999) Fractional Differential Equations. Mathematics in Science and Engineering, Vol. 198, AcademicPress, NewYork/London/Toronto.
[7]  Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993) Fractional Integrals and Derivatives. (Theory and Applications). Gordon and Breach, Switzerland.
[8]  Baleanu, D., Mustafa, O.G. and Agarwal, R.P. (2010) An Existence Result for a Super Linear Fractional Differential Equation. Applied Mathematics Letters, 23, 1129-1132. http://dx.doi.org/10.1016/j.aml.2010.04.049
[9]  Baleanu, D., Agarwal, R.P., Mustafa, O.G. and Cosulschi, M. (2011) Asymptotic Integration of Some Nonlinear Differential Equations with Fractional Time Derivative. Journal of Physics A: Mathematical and Theoretical, 44. http://dx.doi.org/10.1088/1751-8113/44/5/055203
[10]  Baleanu, D., Mustafa, O.G. and Agarwal, R.P. (2010) On the Solution Set for a Class of Sequential Fractional Differential Equations. Journal of Physics A: Mathematical and Theoretical, 43.
[11]  Zhao, X.K., Chai, C.W. and Ge, W.G. (2011) Positive Solutions for Fractional Four-Point Boundary Value Problems. Communications in Nonlinear Science and Numerical Simulation, 16, 3665-3672. http://dx.doi.org/10.1016/j.cnsns.2011.01.002
[12]  Wang, J.H., Xiang, H.J. and Liu, Z.G. (2010) Positive Solution to Nonzero Boundary Value Problem for a Coupled System of Nonlinear Fractional Differential Equations. International Journal of Differential Equations.
[13]  Ahmad, B. and Nieto, J.J. (2009) Existence Results for a Coupled System of Nonlinear Fractional Differential Equations with Three-Point Boundary Conditions. Computers & Mathematics with Applications, 58, 1838-1843. http://dx.doi.org/10.1016/j.camwa.2009.07.091
[14]  Zhang, S.Q. (2006) Positive Solutions for Boundary-Value Problem of Fractional Order. Acta Mathematica Scientia, 36, 1-12.
[15]  Guo, D. and Lakshmikantham, V. (1988) Nonlinear Problem in Abstract Cones. Academic Press, San Diego.
[16]  Webb, J.R.L. and Lan, K.Q. (2006) Eigenvalue Criteria for Existence of Multiple Positive Solutions of Nonlinear Boundary Value Problems of Local and Nonlocal Type. Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center, 27, 91-115.

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