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 Dαn - Σn-1j=1 pj(x)Dαn-j)y = ƒ(x, y). We state various conditions on ƒ and pj's under which this equation has: positive solutions, a unique solution which is positive, and a unique solution which may not be positive.