Abstract
The motive behind this work is to obtain some sufficient conditions for the existence of solution to a nonlinear problem of implicit fractional differential equations (IFDEs) involving integral boundary conditions with p-Laplacian operator, using prior estimate method. The method applied here does not require compactness of the operator, which makes it distinguished from other methods. Besides developing the respective conditions, we also investigate Hyers-Ulam type stability for the solution of the problem under study. The validity of the established results are justified by providing a suitable example.