University of GuilanJournal of Mathematical Modeling2345-394X8420200901Positive solutions for generalized Caputo fractional differential equations with integral boundary conditions393414415710.22124/jmm.2020.16125.1407ENHanan A.WahashDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India0000-0003-1927-7301Satish K.PanchalDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, IndiaMohammed S.AbdoDepartment of Mathematics, Hodeidah University, Al-Hodeidah, Yemen0000-0001-9085-324XJournal Article20200426This article is devoted to the study of a new class of nonlinear fractional-order differential equations with integral boundary conditions involving a generalized version of the Caputo type fractional derivative with respect to another function $h$. In such a path, we transform the proposed problem into an equivalent integral equation. Then we build the upper and lower control functions of the nonlinear term without any monotone requirement except the continuity. By utilizing the method of upper and lower solutions, the fixed point theorems of Schauder and Banach, we obtain the existence and uniqueness of positive solutions for the problem at hand. Finally, we present some examples to illuminate our results.https://jmm.guilan.ac.ir/article_4157_bebd828095aa4e625a009cd6ec2f6d06.pdf