Geodesic
Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients
Electronic journal of differential equations, Tome 2006 (2006)
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.
Classification : 26A33, 34B18
Keywords: Riemann-Liouville fractional derivatives and integrals, normal cone, semi-ordered Banach space, completely continuous operator, equicontinuous set 
@article{EJDE_2006__2006__a6,
     author = {Babakhani,  Azizollah and Daftardar-Gejji,  Varsha},
     title = {Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1116.26003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a6/}
}
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Babakhani,  Azizollah; Daftardar-Gejji,  Varsha. Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a6/