Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 129, pp. 1-12.

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

Authors: Azizollah Babakhani  (Univ. of Mazanderan, Babol, Iran)
         Varsha Daftardar-Gejji (Univ. of Pune, India)

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.