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.