Electron. J. Diff. Eqns., Vol. 2006(2006), No. 129, pp. 1-12.

Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients

Azizollah Babakhani, Varsha Daftardar-Gejji

Abstract:
In the present paper we discuss the existence of positive solutions in the case of multi-term non-autonomous fractional differential equations with polynomial coefficients; the constant coefficient case has been studied in [2]. We consider the equation
$$ \Big(D^{\alpha_n} -\sum_{j = 1}^{n - 1} p_j(x)D^{\alpha_{n - j}}\Big)y = f(x, y). $$
We state various conditions on $f$ and $p_j$'s under which this equation has: positive solutions, a unique solution which is positive, and a unique solution which may not be positive.

Submitted July 27, 2005. Published October 16, 2006.
Math Subject Classifications: 26A33, 34B18.
Key Words: Riemann-Liouville fractional derivatives and integrals; normal cone; semi-ordered Banach space; completely continuous operator; equicontinuous set.

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Azizollah Babakhani
Department of Mathematics
University of Mazanderan, Babol, Iran
email: babakhani@nit.ac.ir
Varsha Daftardar-Gejji
Department of Mathematics, University of Pune
Ganeshkhind, Pune - 411007, India
email: vsgejji@math.unipune.ernet.in

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