Geodesic
Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     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/