“…Integral boundary conditions of fractional problems are approached by various researchers by applying different fixed point theorems, iterative technique, and upper and lower solutions method. We refer the reader to a series of articles [22,23,37,29,28,35,6,33,3,10,9,32,20,34,31,5]. Another aspect of stability analysis has been taken up by a number of mathematicians called "Ulam-Hyers stability" this concept was introduced in the mid of 19 th century and recently it is a one of the most important subjects in the mathematical analysis area.…”