Positive solutions of boundary value problems for fractional differential equations involving the generalized proportional derivatives Generalized proportional fractional BVP

Abstract

This paper is concerned with the existence and uniqueness of positive solutions of boundary value problems for fractional differential equations involving the generalized proportional derivatives of Caputo type. The investigation of the proposed BVP depends on the properties of the Green function, the method of upper and lower solutions, and the fixed point theorems due to Schauder and Banach. An example is proposed to clarify the applicability of the theoretical results.