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

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.

Keywords

• Riemann-Liouville fractional derivatives and integrals
• normal cone
• semi-ordered Banach space
• completely continuous operator
• equicontinuous set.